Time, Speed, and Distance: Formulas, Problems, and Solutions for Competitive Exams

Answers to Time, Speed, and Distance Questions:

1. A car travels 120 km in 2 hours. What is its speed?

• Answer: $$\text{Speed} = \frac{120}{2} = 60 \, \text{km/h}$$Speed=2120​=60km/h

2. A person runs 5 km in 50 minutes. What is his speed in km/h?

• Answer: $$\text{Speed} = \frac{5}{\frac{50}{60}} = \frac{5}{\frac{5}{6}} = 6 \, \text{km/h}$$Speed=6050​5​=65​5​=6km/h

3. A train travels at a speed of 72 km/h. How much time will it take to cover 180 km?

• Answer: $$\text{Time} = \frac{180}{72} = 2.5 \, \text{hours}$$Time=72180​=2.5hours

4. A man walks 100 meters in 2 minutes. What is his speed in m/s?

• Answer: $$\text{Speed} = \frac{100}{2 \times 60} = \frac{100}{120} = 0.833 \, \text{m/s}$$Speed=2×60100​=120100​=0.833m/s

5. A cyclist covers a distance of 30 km in 2 hours. What is his speed in km/h?

• Answer: $$\text{Speed} = \frac{30}{2} = 15 \, \text{km/h}$$Speed=230​=15km/h

6. Two cars are moving in the same direction. One travels at 60 km/h and the other at 80 km/h. How long will it take for the faster car to overtake the slower one?

• Answer:
  Relative speed = $80 – 60 = 20 \, \text{km/h}$80−60=20km/h.
  Time taken to overtake = $\frac{d}{20}$20d​, where $d$d is the distance between the two cars. If the distance is not specified, you can assume $d = 1$d=1 km for simplicity, and the time would be: $$\text{Time} = \frac{1}{20} \, \text{hours} = 3 \, \text{minutes}.$$Time=201​hours=3minutes.

7. Two trains are moving towards each other. One travels at 50 km/h and the other at 70 km/h. If the distance between them is 420 km, how much time will it take for them to meet?

• Answer:
  Combined speed = $50 + 70 = 120 \, \text{km/h}$50+70=120km/h.
  Time taken to meet = $\frac{420}{120} = 3.5 \, \text{hours}$120420​=3.5hours.

8. A boat goes downstream for 15 km and returns to the starting point in 3 hours. If the speed of the boat in still water is 5 km/h and the speed of the current is 1 km/h, what is the time taken for the downstream trip?

• Answer:
  Downstream speed = $5 + 1 = 6 \, \text{km/h}$5+1=6km/h.
  Time for downstream trip = $\frac{15}{6} = 2.5 \, \text{hours}$615​=2.5hours.

9. Two persons start walking at the same time in opposite directions. If one walks at 6 km/h and the other at 8 km/h, how long will it take for them to be 70 km apart?

• Answer:
  Relative speed = $6 + 8 = 14 \, \text{km/h}$6+8=14km/h.
  Time taken = $\frac{70}{14} = 5 \, \text{hours}$1470​=5hours.

10. A man covers a distance of 100 km at a speed of 20 km/h. Another man covers the same distance at a speed of 25 km/h. How long will it take the second man to finish the journey?

• Answer:
  Time taken by second man = $\frac{100}{25} = 4 \, \text{hours}$25100​=4hours.

11. A person travels from A to B at 40 km/h and returns from B to A at 60 km/h. What is his average speed for the round trip?

• Answer:
  Average speed = $\frac{2 \times 40 \times 60}{40 + 60} = \frac{4800}{100} = 48 \, \text{km/h}$40+602×40×60​=1004800​=48km/h.

12. A train takes 30 seconds to pass a platform of 100 meters. If the speed of the train is 72 km/h, what is the length of the train?

• Answer:
  Convert speed to m/s: $72 \, \text{km/h} = \frac{72 \times 1000}{3600} = 20 \, \text{m/s}$72km/h=360072×1000​=20m/s.
  Distance covered in 30 seconds = $20 \times 30 = 600 \, \text{m}$20×30=600m.
  Length of train = $600 – 100 = 500 \, \text{meters}$600−100=500meters.

13. A boat can travel 12 km upstream in 4 hours and 12 km downstream in 3 hours. Find the speed of the boat in still water and the speed of the stream.

• Answer:
  Speed of boat in still water = $\frac{12}{\frac{4}{12} + \frac{3}{12}} = 4 \, \text{km/h}$124​+123​12​=4km/h.
  Speed of stream = $\frac{12}{4} – \frac{12}{3} = 2 \, \text{km/h}$412​−312​=2km/h.

14. A cyclist covers a distance of 36 km in 2 hours. How long will it take to cover 45 km at the same speed?

• Answer:
  Speed = $\frac{36}{2} = 18 \, \text{km/h}$236​=18km/h.
  Time for 45 km = $\frac{45}{18} = 2.5 \, \text{hours}$1845​=2.5hours.

15. A train 200 meters long is running at a speed of 36 km/h. How long will it take to cross a bridge 100 meters long?

• Answer:
  Convert speed to m/s: $36 \, \text{km/h} = \frac{36 \times 1000}{3600} = 10 \, \text{m/s}$36km/h=360036×1000​=10m/s.
  Total distance to be covered = $200 + 100 = 300 \, \text{meters}$200+100=300meters.
  Time taken = $\frac{300}{10} = 30 \, \text{seconds}$10300​=30seconds.

16. A person travels from A to B at 50 km/h and from B to A at 40 km/h. What is his average speed for the entire journey?

• Answer:
  Average speed = $\frac{2 \times 50 \times 40}{50 + 40} = \frac{4000}{90} \approx 44.44 \, \text{km/h}$50+402×50×40​=904000​≈44.44km/h.

17. A person travels 60 km in 1 hour. How far will he travel in 3 hours at the same speed?

• Answer:
  Distance = $60 \times 3 = 180 \, \text{km}$60×3=180km.

18. A man covers a distance of 100 km at a speed of 20 km/h. Another man covers the same distance at a speed of 25 km/h. How long will it take the second man to finish the journey?

• Answer:
  Time taken by second man = $\frac{100}{25} = 4 \, \text{hours}$25100​=4hours.

19. A train crosses a man walking at 5 km/h in 20 seconds. If the length of the train is 100 meters, what is the speed of the train?

• Answer:
  Relative speed = $\frac{100}{20} \times 3600 = 18 \, \text{km/h}$20100​×3600=18km/h.
  Speed of train = $18 + 5 = 23 \, \text{km/h}$18+5=23km/h.

20. A car travels at a speed of 50 km/h for the first 30 minutes, 60 km/h for the next 30 minutes, and 70 km/h for the next hour. What is the average speed of the car for the entire journey?

• Answer:
  Total distance = $\frac{50}{2} + \frac{60}{2} + 70 = 25 + 30 + 70 = 125 \, \text{km}$250​+260​+70=25+30+70=125km.
  Total time = $\frac{30}{60} + \frac{30}{60} + 1 = 2 \, \text{hours}$6030​+6030​+1=2hours.
  Average speed = $\frac{125}{2} = 62.5 \, \text{km/h}$2125​=62.5km/h.

21. A person runs at a speed of 10 m/s for 5 minutes. How much distance does he cover?

Answer:
Distance = $10 \times 60 \times 5 = 3000 \, \text{m} = 3 \, \text{km}$10×60×5=3000m=3km.