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If a race car zooms 120 miles in 2 hours, how far does it go in just 1 hour?

It travels 60 miles each hour, which we call its **speed**.

**Speed** tells you how much **distance** you cover in a set amount of **time**.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Speed, Distance, and Time</title>
  <link rel="stylesheet" href="{{VENDOR_CDN}}/katex.min.css">
  <script src="{{VENDOR_CDN}}/katex.min.js"></script>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 16px;
      gap: 16px;
    }

    /* Preset selector tabs */
    .tabs {
      display: flex;
      gap: 8px;
      width: 100%;
      max-width: 520px;
      justify-content: center;
    }
    .tab-btn {
      flex: 1;
      padding: 8px 12px;
      font-size: 14px;
      font-weight: 600;
      background: #ffffff;
      border: 2px solid #e2e8f0;
      border-radius: 10px;
      color: #64748b;
      cursor: pointer;
      text-align: center;
      transition: background 0.2s, color 0.2s, border-color 0.2s, box-shadow 0.2s;
    }
    .tab-btn.active {
      background: #22b7ff;
      border-color: #22b7ff;
      color: #ffffff;
      box-shadow: 0 4px 12px rgba(34, 183, 255, 0.25);
    }

    /* Track & Simulation Arena */
    .stage {
      width: 100%;
      max-width: 520px;
      background: #ffffff;
      border-radius: 16px;
      padding: 24px 20px 20px;
      box-shadow: 0 4px 20px rgba(0, 0, 0, 0.05);
      display: flex;
      flex-direction: column;
      gap: 20px;
    }

    .track-container {
      position: relative;
      height: 64px;
      display: flex;
      align-items: flex-end;
    }
    .track-line {
      position: absolute;
      bottom: 24px;
      left: 20px;
      right: 20px;
      height: 4px;
      background: #e2e8f0;
      border-radius: 2px;
    }
    .track-fill {
      position: absolute;
      left: 0;
      top: 0;
      bottom: 0;
      width: 0%;
      background: rgba(34, 183, 255, 0.2);
      border-radius: 2px;
      transition: width 0.1s linear;
    }
    .ticks {
      position: absolute;
      bottom: 0;
      left: 20px;
      right: 20px;
      display: flex;
      justify-content: space-between;
      pointer-events: none;
    }
    .tick {
      display: flex;
      flex-direction: column;
      align-items: center;
      font-size: 12px;
      color: #94a3b8;
      font-weight: 500;
    }
    .tick::before {
      content: "";
      width: 2px;
      height: 8px;
      background: #cbd5e1;
      margin-bottom: 4px;
    }

    .runner {
      position: absolute;
      bottom: 24px;
      left: 20px;
      font-size: 28px;
      line-height: 1;
      transform: translate(-50%, -2px);
      transition: left 0.1s linear;
      will-change: left;
    }

    /* Live Data Badges */
    .data-row {
      display: flex;
      justify-content: space-between;
      gap: 8px;
    }
    .metric-badge {
      flex: 1;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 8px 10px;
      text-align: center;
    }
    .metric-title {
      font-size: 11px;
      text-transform: uppercase;
      font-weight: 700;
      color: #94a3b8;
      letter-spacing: 0.5px;
    }
    .metric-value {
      font-size: 16px;
      font-weight: 700;
      color: #1e2945;
      margin-top: 2px;
    }

    /* Math Formula Display */
    .formula-card {
      width: 100%;
      max-width: 520px;
      background: #f0f9ff;
      border: 1px solid #bae6fd;
      border-radius: 12px;
      padding: 12px 16px;
      display: flex;
      align-items: center;
      justify-content: center;
      min-height: 52px;
    }

    /* Controls */
    .controls {
      display: flex;
      gap: 8px;
      justify-content: center;
    }
    .action-btn {
      padding: 8px 20px;
      font-size: 14px;
      font-weight: 600;
      border-radius: 8px;
      border: none;
      background: #1e2945;
      color: #ffffff;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 6px;
      transition: opacity 0.2s;
    }
    .action-btn:active {
      opacity: 0.8;
    }
  </style>
</head>
<body>

  
  <div class="tabs">
    <button class="tab-btn active" data-preset="0">60 m in 2 s</button>
    <button class="tab-btn" data-preset="1">60 m in 3 s</button>
    <button class="tab-btn" data-preset="2">30 m in 3 s</button>
  </div>

  
  <div class="stage">
    <div class="track-container">
      <div class="track-line">
        <div class="track-fill" id="trackFill"></div>
      </div>
      <div class="runner" id="runner">🚗</div>
      <div class="ticks">
        <div class="tick">0m</div>
        <div class="tick">15m</div>
        <div class="tick">30m</div>
        <div class="tick">45m</div>
        <div class="tick">60m</div>
      </div>
    </div>

    
    <div class="data-row">
      <div class="metric-badge">
        <div class="metric-title">Distance</div>
        <div class="metric-value" id="valDist">0 m</div>
      </div>
      <div class="metric-badge">
        <div class="metric-title">Time</div>
        <div class="metric-value" id="valTime">0.0 s</div>
      </div>
      <div class="metric-badge">
        <div class="metric-title">Speed</div>
        <div class="metric-value" id="valSpeed">--</div>
      </div>
    </div>
  </div>

  
  <div class="formula-card" id="formulaCard"></div>

  
  <div class="controls">
    <button class="action-btn" id="playBtn">▶ Run</button>
  </div>

  <script>
    const presets = [
      { dist: 60, time: 2 },
      { dist: 60, time: 3 },
      { dist: 30, time: 3 }
    ];

    let currentPreset = 0;
    let animId = null;
    let startTime = null;

    const runner = document.getElementById('runner');
    const trackFill = document.getElementById('trackFill');
    const valDist = document.getElementById('valDist');
    const valTime = document.getElementById('valTime');
    const valSpeed = document.getElementById('valSpeed');
    const formulaCard = document.getElementById('formulaCard');
    const playBtn = document.getElementById('playBtn');
    const tabBtns = document.querySelectorAll('.tab-btn');

    function updateFormula(d, t, s, isFinal) {
      if (!window.katex) return;
      if (!isFinal) {
        katex.render(
          `\\text{Speed} = \\frac{\\text{Distance}}{\\text{Time}} = \\frac{${d}\\text{ m}}{${t}\\text{ s}}`,
          formulaCard,
          { throwOnError: false }
        );
      } else {
        katex.render(
          `\\text{Speed} = \\frac{${d}\\text{ m}}{${t}\\text{ s}} = \\mathbf{${s}\\text{ m/s}}`,
          formulaCard,
          { throwOnError: false }
        );
      }
    }

    function renderStatic(idx) {
      cancelAnimationFrame(animId);
      const p = presets[idx];
      const maxTrackDist = 60;
      const pct = (p.dist / maxTrackDist) * 100;
      
      runner.style.left = `calc(20px + ${pct}% * 0.88)`;
      trackFill.style.width = `${pct}%`;
      
      const speed = p.dist / p.time;
      valDist.textContent = `${p.dist} m`;
      valTime.textContent = `${p.time.toFixed(1)} s`;
      valSpeed.textContent = `${speed} m/s`;

      updateFormula(p.dist, p.time, speed, true);
      playBtn.textContent = "↺ Replay";
    }

    function startAnimation(idx) {
      cancelAnimationFrame(animId);
      const p = presets[idx];
      const speed = p.dist / p.time;
      const durationMs = p.time * 1000;
      const maxTrackDist = 60;

      runner.style.left = '20px';
      trackFill.style.width = '0%';
      valDist.textContent = '0 m';
      valTime.textContent = '0.0 s';
      valSpeed.textContent = '...';
      updateFormula(p.dist, p.time, speed, false);
      playBtn.textContent = "⏸ Running";

      startTime = performance.now();

      function step(now) {
        const elapsed = now - startTime;
        const progress = Math.min(elapsed / durationMs, 1);

        const currentD = (progress * p.dist).toFixed(0);
        const currentT = (progress * p.time).toFixed(1);
        const pct = progress * (p.dist / maxTrackDist) * 100;

        runner.style.left = `calc(20px + ${pct}% * 0.88)`;
        trackFill.style.width = `${pct}%`;
        valDist.textContent = `${currentD} m`;
        valTime.textContent = `${currentT} s`;

        if (progress < 1) {
          animId = requestAnimationFrame(step);
        } else {
          valDist.textContent = `${p.dist} m`;
          valTime.textContent = `${p.time.toFixed(1)} s`;
          valSpeed.textContent = `${speed} m/s`;
          updateFormula(p.dist, p.time, speed, true);
          playBtn.textContent = "↺ Replay";
        }
      }

      animId = requestAnimationFrame(step);
    }

    tabBtns.forEach(btn => {
      btn.addEventListener('click', () => {
        tabBtns.forEach(b => b.classList.remove('active'));
        btn.classList.add('active');
        currentPreset = parseInt(btn.dataset.preset, 10);
        startAnimation(currentPreset);
      });
    });

    playBtn.addEventListener('click', () => {
      startAnimation(currentPreset);
    });

    // Initialize
    window.addEventListener('DOMContentLoaded', () => {
      startAnimation(0);
    });
  </script>
</body>
</html>

To find speed, divide distance by time: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$.

What happens if a trip takes minutes instead of whole hours?

Because 1 hour has **60 minutes**, you divide minutes by 60 to write them as a **fractional hour**.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <link rel="stylesheet" href="{{VENDOR_CDN}}/katex.min.css">
  <script src="{{VENDOR_CDN}}/katex.min.js"></script>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif; }
    body {
      background: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 12px;
      min-height: 100%;
    }
    .container {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 14px;
    }
    .btn-row {
      display: flex;
      flex-wrap: wrap;
      gap: 8px;
      justify-content: center;
    }
    .preset-btn {
      background: #ffffff;
      border: 2px solid #e2e8f0;
      border-radius: 20px;
      padding: 6px 14px;
      font-size: 14px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
      transition: all 0.2s ease;
    }
    .preset-btn.active {
      background: #22b7ff;
      border-color: #22b7ff;
      color: #ffffff;
      box-shadow: 0 2px 8px rgba(34, 183, 255, 0.35);
    }
    .visual-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 20px;
      width: 100%;
    }
    .clock-box {
      width: 150px;
      height: 150px;
      flex-shrink: 0;
      position: relative;
    }
    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }
    .math-card {
      flex: 1;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 14px 16px;
      box-shadow: 0 2px 6px rgba(0,0,0,0.04);
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 110px;
    }
    .slider-wrap {
      width: 100%;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 6px;
    }
    .range-slider {
      width: 90%;
      height: 8px;
      border-radius: 4px;
      background: #e2e8f0;
      outline: none;
      -webkit-appearance: none;
      cursor: pointer;
    }
    .range-slider::-webkit-slider-thumb {
      -webkit-appearance: none;
      width: 22px;
      height: 22px;
      border-radius: 50%;
      background: #22b7ff;
      box-shadow: 0 2px 6px rgba(34, 183, 255, 0.4);
      cursor: pointer;
    }
    .range-slider::-moz-range-thumb {
      width: 22px;
      height: 22px;
      border-radius: 50%;
      background: #22b7ff;
      box-shadow: 0 2px 6px rgba(34, 183, 255, 0.4);
      border: none;
      cursor: pointer;
    }
    .formula-line {
      font-size: 19px;
      color: #1e2945;
    }
  </style>
</head>
<body>
  <div class="container">
    <div class="btn-row">
      <button class="preset-btn" onclick="setTime(15)">15 min</button>
      <button class="preset-btn active" onclick="setTime(30)">30 min</button>
      <button class="preset-btn" onclick="setTime(45)">45 min</button>
      <button class="preset-btn" onclick="setTime(20)">20 min</button>
      <button class="preset-btn" onclick="setTime(60)">60 min</button>
    </div>

    <div class="visual-row">
      <div class="clock-box">
        <svg viewBox="0 0 160 160">
          <circle cx="80" cy="80" r="70" fill="#f8fafc" stroke="#cbd5e1" stroke-width="4"/>
          
          <line x1="80" y1="14" x2="80" y2="22" stroke="#94a3b8" stroke-width="3" stroke-linecap="round"/>
          <line x1="146" y1="80" x2="138" y2="80" stroke="#94a3b8" stroke-width="3" stroke-linecap="round"/>
          <line x1="80" y1="146" x2="80" y2="138" stroke="#94a3b8" stroke-width="3" stroke-linecap="round"/>
          <line x1="14" y1="80" x2="22" y2="80" stroke="#94a3b8" stroke-width="3" stroke-linecap="round"/>
          
          
          <path id="sector" fill="#22b7ff" opacity="0.35" d=""></path>
          
          
          <line id="minuteHand" x1="80" y1="80" x2="80" y2="24" stroke="#0284c7" stroke-width="4" stroke-linecap="round"/>
          <circle cx="80" cy="80" r="5" fill="#0284c7"/>
          
          
          <text x="80" y="34" text-anchor="middle" font-size="11" fill="#64748b" font-weight="bold">60m</text>
          <text x="130" y="84" text-anchor="middle" font-size="11" fill="#64748b" font-weight="bold">15m</text>
          <text x="80" y="132" text-anchor="middle" font-size="11" fill="#64748b" font-weight="bold">30m</text>
          <text x="30" y="84" text-anchor="middle" font-size="11" fill="#64748b" font-weight="bold">45m</text>
        </svg>
      </div>

      <div class="math-card">
        <div id="mathTarget" class="formula-line"></div>
      </div>
    </div>

    <div class="slider-wrap">
      <input type="range" id="minRange" class="range-slider" min="5" max="60" step="5" value="30" oninput="onSlide(this.value)">
    </div>
  </div>

  <script>
    function gcd(a, b) {
      return b === 0 ? a : gcd(b, a % b);
    }

    function renderMath(mins) {
      const g = gcd(mins, 60);
      const num = mins / g;
      const den = 60 / g;
      const dec = (mins / 60);
      const decStr = Number.isInteger(dec) ? dec.toString() : (Math.round(dec * 1000) / 1000).toString();

      let expr = `\\frac{${mins}\\text{ min}}{60\\text{ min}}`;
      if (g > 1 && !(num === mins && den === 60)) {
        if (num === 1 && den === 1) {
          expr += ` = 1\\text{ hr}`;
        } else {
          expr += ` = \\frac{${num}}{${den}} = ${decStr}\\text{ hr}`;
        }
      } else {
        expr += ` = ${decStr}\\text{ hr}`;
      }

      const el = document.getElementById('mathTarget');
      if (window.katex) {
        katex.render(expr, el, { throwOnError: false });
      } else {
        el.textContent = `${mins}/60 = ${decStr} hr`;
      }
    }

    function updateClock(mins) {
      const angle = (mins / 60) * 360;
      const rad = (angle - 90) * (Math.PI / 180);
      const cx = 80, cy = 80, r = 68;

      // Hand line
      const hx = cx + r * Math.cos(rad);
      const hy = cy + r * Math.sin(rad);
      const hand = document.getElementById('minuteHand');
      hand.setAttribute('x2', hx);
      hand.setAttribute('y2', hy);

      // Sector path
      const sector = document.getElementById('sector');
      if (mins >= 60) {
        sector.setAttribute('d', `M ${cx} ${cy - r} A ${r} ${r} 0 1 1 ${cx - 0.01} ${cy - r} Z`);
      } else if (mins <= 0) {
        sector.setAttribute('d', '');
      } else {
        const largeArc = angle > 180 ? 1 : 0;
        sector.setAttribute('d', `M ${cx} ${cy} L ${cx} ${cy - r} A ${r} ${r} 0 ${largeArc} 1 ${hx} ${hy} Z`);
      }
    }

    function setTime(mins) {
      mins = parseInt(mins, 10);
      document.getElementById('minRange').value = mins;
      
      document.querySelectorAll('.preset-btn').forEach(btn => {
        const btnVal = parseInt(btn.textContent, 10);
        btn.classList.toggle('active', btnVal === mins);
      });

      updateClock(mins);
      renderMath(mins);
    }

    function onSlide(val) {
      const mins = parseInt(val, 10);
      document.querySelectorAll('.preset-btn').forEach(btn => {
        const btnVal = parseInt(btn.textContent, 10);
        btn.classList.toggle('active', btnVal === mins);
      });
      updateClock(mins);
      renderMath(mins);
    }

    // Initial render
    setTime(30);
  </script>
</body>
</html>

For example, 30 minutes is $\frac{30}{60} = 0.5$ hours, and 15 minutes is $\frac{15}{60} = 0.25$ hours.

Can we use these fraction hours to solve a real trip problem?

A train travels **90 miles** in **1 hour and 30 minutes**.

First, write 1 hour and 30 minutes as $1.5$ hours.

Next, divide distance by time: $\text{Speed} = \frac{90}{1.5} = 60\text{ miles per hour}$.

Why must we avoid writing 1 hour and 30 minutes as 1.3 hours?

A common mistake is writing 30 minutes as $.30$, but hours are based on **60 minutes**, not 100.

Always divide your minutes by 60 before doing the math.

Now try this: if you ride a bicycle at 12 miles per hour for 45 minutes, how many miles do you go?

math

Solving Compound Measure Problems: Speed, Distance, and Time. Apply multi-step calculations to solve complex journey and rate word problems in varied real-world contexts.

Speed, Distance and Time - National 4 / Fourth Level Maths

Speed, Distance, and Time Practice Questions & Video Tutorials

Exploring Rates and Compound Measures: Speed, Distance, and Time

Although labeled with an Early Level header in the query prompt, the benchmark standard MNU 4-08a and topic 'Solving Compound Measure Problems: Speed, Distance, and Time' belong pedagogically to Scottish Curriculum for Excellence (CfE) Fourth Level (BGE S1–S3 / Key Stage 3 / Grades 7–8). Effective instruction prioritizes connecting direct proportionality to rate triangles and double number lines, emphasizing deliberate practice with base-60 to base-10 time conversions before calculation.

Solving Compound Measure Problems: Speed, Distance, and Time

The Speed Formula

Turning Minutes into Hours

Finding Speed with Fractions