# Time Speed Distance

12
 Question 1
Samuel covers the distance from his home to his office at a speed of 25 km/hr and comes back at a speed of 4 km/hr. He completes the whole journey within 5 hours 48 minutes. Find out the distance from his home to office:
 A 20 km B 18 km C 15 km D 25 km
Time Speed Distance
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Question 1 Explanation:
Let the speed of travelling to office and back to home be x and y respectively. So, his average speed is = 2xy / (x+y) = (2 × 25 × 4) / (25 + 4) = 200/29 km/hr He covers the whole journey in 5 hours 48 minutes = 5⅘ = 29/5 hrs Therefore, total distance covered = (200/29 × 29/5) = 40 km So, the distance from his home to office = 40/2 = 20 km
 Question 2
If John walks at the speed of 5 km/h, he reaches his office 7 minutes late. However, if he walks at the speed of 6 km/h, he reaches his office 5 minutes early. How far is his office from his home?
 A 9 B 8 C 10 D 6
Time Speed Distance
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Question 2 Explanation:
Let the distance of John’s office from his home be x. The time difference when covering the distance x at the two different speeds = 5 - (-7) = 12 min = 1/5 hr ⇒ x/5 - x/6 = 1/5 ⇒ (6x - 5x)/30 = 1/5 ⇒ x = 6. So, his office is 6 km far from his home.
 Question 3
A policeman sees a thief at a distance of 100 meters and starts to chase him. The thief sees him and starts to run too. If the thief is running at the speed of 8 km/hr and the policeman is running at the speed of 10 km/hr, find out the distance covered by the thief before the policeman catches him.
 A 250 meters B 400 meters C 450 meters D 401 meters
Time Speed Distance
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Question 3 Explanation:
We can safely assume that the policeman is running in the same direction as the thief. Speed of policeman w.r.t thief = (10 - 8) = 2 km/hr. Time taken by policeman to cover the 100m distance between him and the thief = (100/1000) / 2 = 1/20 hr. Therefore, the distance covered by thief in 1/20 hrs = 8 × 1/20 = 2/5 km = 400 meters.
 Question 4
Paul has to travel 24 km. After walking for 1 hour 40 minutes he sees that he has covered 5/7 of the distance left to cover. Find out Paul’s speed in meters per second.
 A 5/3 m/s B 7/5 m/s C 2/3 m/s D 8/5 m/s
Time Speed Distance
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Question 4 Explanation:
Let the required speed be x km/hr. Distance covered by Paul in 1 hr 40 min = x × 100/60 = 5x/3 km. Remaining distance = (24 - 5x/3) km. Therefore, 5x/3 = 5/7 × (24 - 5x/3) ⇒ 7/5 × 5x/3 = 24 - 5x/3 ⇒ 7x/3 = (72 - 5x)/3 ⇒ 7x = 72 - 5x ⇒ 12x = 72 ⇒ x = 6. Paul's speed in meters per second = 6 × 5/18 = 5/3 m/s.
 Question 5
The ratio of the speed of two trains is 7:8. If the second train covers 400 km in 4 h, find out the speed of the first train.
 A 69.4 km/h B 78.6 km/h C 87.5 km/h D 40.5 km/h
Ratio and Proportion    Time Speed Distance
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Question 5 Explanation:
Let the speed of the two trains be 7x and 8x. Then, 8x = 400 / 4 ⇒ 8x = 100 ⇒ x = 12.5 km/h. Hence, speed of the first train = 7x = 7 × 12.5 = 87.5 km/h.
 Question 6
Rajdhani Express halts for 3 minutes every time it covers a distance of 75 km. If the train runs at a speed of 100 km/h and the destination is 600 km away from the source, find out the time taken to reach the destination station from the source station.
 A 6 h 23 min B 6 h 22 min C 6 h 21 min D 6 h 24 min
Time Speed Distance
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Question 6 Explanation:
Since the train runs at a speed of 100 km/h, the time taken to cover 600 km = 600/100 = 6 h. Number of times the train halts = 600/75 - 1 = 7. Since the train halts for 3 minutes at each stop, the time spent waiting = 7 * 3 = 21 min. Therefore, total time taken = 6 h 21 min.
 Question 7
Max completes his journey at an average speed of 9 km/h. He covers the first 9 km at a speed of 6 km/h and he takes 1·5 hours to cover the remaining distance. Find out the speed at which he covered the remaining distance.
 A 11 km/h B 12 km/h C 13 km/h D 15 km/h
Time Speed Distance
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Question 7 Explanation:
Let the required speed be x km/h. Total time taken to finish his journey = (9/6 + 1·5) = 3 hours. Total distance = 9 + 1·5x km. Given, average speed = 9 km/h. Therefore, (9 + 1·5x)/3 = 9 ⇒ 9 + 1·5x = 27 ⇒ 1·5x = 18 ⇒ x = 12 km/h.
 Question 8
Peter and Beckon start to walk in the same direction together. If Peter's speed is 5 km/h and Beckon's speed is 6 km/h, find out the time duration after which they are 17 km apart.
 A 17 B 15 C 19 D 20
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Question 8 Explanation:
In 1 hour Peter covers 5 km and Beckon covers 6 km. So, they are 1 km apart after 1 hour. Therefore, they are 17 km apart after 17 hours.
 Question 9
A car covers a distance of 450m in 90 secs. What is the speed in km/hr?
 A 20 B 5 C 10 D 18
Time Speed Distance
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Question 9 Explanation:
Speed = distance/time = 450m/90sec = 5m/sec = (5*60*60)/(1000) = 18 Km/hr.
 Question 10
A train covers a journey of 4 stations connected to form a square at speeds of 20, 40, 60 and 80 km/hr. What is the average speed of train for this journey?
 A 38.4 B 100 C 80.4 D 160
Time Speed Distance
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Question 10 Explanation:
Speed = distance/time Say, side of square = y km time t1 = y/20 t2 = y/40, t3 = y/60 and t4 = y/80 Total time = (12+6+4+3)y/240 speed = total distance/total time = 4y/(t1+t2+t3+t4) = 4y*240/25y = 38.4 km/hr
There are 20 questions to complete.
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