Rates, Work & Speed • Topic 3 of 4

Speed, Distance & Time

Everything here comes from distance = speed × time, rearranged as needed. Keep units consistent — a speed in km/h needs a time in hours, so convert 45 minutes to 0.75 h before multiplying. Two GRE staples deserve special attention. Relative speed: two objects moving toward each other close the gap at the sum of their speeds, while one chasing another closes it at the difference. So two trains approaching at 50 and 70 km/h close 120 km each hour; a car at 80 overtaking one at 60 gains 20 km/h. The other staple is the "same time" setup, where two travellers meet — set their distances to add up to the total, or set them equal for a catch-up. Because the calculator is basic, the GRE keeps these numbers friendly; your job is to translate the words into the right sum or difference of speeds.

✅ Solved examples

1. A train travels at 72 km/h for 45 minutes. How far does it go?
Convert time: 45 min = 0.75 h. Distance = 72 × 0.75 = 54 km.
2. Two cyclists start 90 km apart and ride toward each other at 12 and 18 km/h. When do they meet?
Closing speed = 12 + 18 = 30 km/h. Time = 90/30 = 3 hours.
3. A car leaves at 60 km/h. Two hours later a second car chases it at 80 km/h. How long until the second catches the first?
Head start = 60 × 2 = 120 km. Gain = 80 − 60 = 20 km/h. Catch-up time = 120/20 = 6 hours.
4. A 180 m train passes a stationary pole in 9 seconds. Find its speed in km/h.
Speed = 180/9 = 20 m/s. Convert: 20 × 3.6 = 72 km/h.

✏️ Practice — try these, take hints as needed

1. A bus covers 210 km in 3.5 hours. Find its average speed.
speed = distance / time.
210 / 3.5.
Simplify.
60 km/h
2. How long does a 150 km trip take at 40 km/h? Give the answer in hours and minutes.
time = distance / speed.
150/40 = 3.75 h.
0.75 h = 45 min.
3 hours 45 minutes
3. Two trains 300 km apart move toward each other at 40 and 60 km/h. When do they meet?
Add the speeds.
Closing speed = 100 km/h.
300/100.
3 hours
4. A runner at 10 km/h chases another 5 km ahead moving at 8 km/h. Catch-up time?
Relative speed = 10 − 8.
= 2 km/h.
5/2.
2.5 hours
5. A 250 m train crosses a 150 m bridge in 20 seconds. Find its speed in m/s.
Distance = train + bridge.
250 + 150 = 400 m.
400/20.
20 m/s

📝 Topic test — 8 questions

Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.

Loading questions…
← Average Rate Combined Work →