Time, Speed & Distance • Topic 1 of 4

Speed Basics

Everything starts with Speed = Distance ÷ Time, and the two rearrangements Distance = Speed × Time and Time = Distance ÷ Speed. The first CAT survival skill is unit fluency: convert km/h to m/s by multiplying by 5/18, and m/s to km/h by multiplying by 18/5. A train at 72 km/h is moving 72 × 5/18 = 20 m/s — useful because crossing-the-pole questions are set in metres and seconds. The second key idea is inverse proportion: when distance is fixed, speed and time vary inversely, so if speed rises by 25% (becomes 5/4), time falls to 4/5 of the original. CAT loves this ratio shortcut because it avoids plugging in actual numbers. Always read the units in the question before computing — mixing km/h with metres is the most common silent error.

✅ Solved examples

1. Convert 90 km/h to m/s.
90 × 5/18 = 5 × 5 = 25 m/s.
2. A car covers 240 km in 4 hours. Find its speed in km/h and in m/s.
Speed = 240/4 = 60 km/h. In m/s: 60 × 5/18 = 50/3 ≈ 16.67 m/s.
3. A cyclist increases speed by 20%. By what percent does the time for a fixed distance fall?
Speed becomes 6/5, so time becomes 5/6 ⇒ a fall of 1/6 ≈ 16⅔%.
4. A man walks at 5 km/h and reaches office 6 min late; at 6 km/h he is 4 min early. Find the distance.
Time gap = 10 min = 1/6 h. d/5 − d/6 = 1/6 ⇒ d(1/30) = 1/6 ⇒ d = 5 km.

✏️ Practice — try these, take hints as needed

1. Convert 54 km/h to m/s.
Multiply by 5/18.
54 × 5/18.
3 × 5.
15 m/s
2. Convert 25 m/s to km/h.
Multiply by 18/5.
25 × 18/5.
5 × 18.
90 km/h
3. A train travels 360 km in 5 hours. Find its speed.
Speed = distance/time.
360/5.
Divide.
72 km/h
4. A bus reduces speed by 25%. By what percent does the time for a fixed route increase?
Speed becomes 3/4.
Time becomes 4/3.
Increase = 1/3.
33⅓%
5. A man walking at 4 km/h reaches 5 min late; at 5 km/h he is 4 min early. Find the distance.
Gap = 9 min = 3/20 h.
d/4 − d/5 = 3/20.
d(1/20) = 3/20.
3 km

📝 Topic test — 8 questions

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