# Time Speed Distance

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:

20 km | |

18 km | |

15 km | |

25 km |

**Time Speed Distance**

**Discuss it**

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?

9 | |

8 | |

10 | |

6 |

**Time Speed Distance**

**Discuss it**

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.

250 meters | |

400 meters | |

450 meters | |

401 meters |

**Time Speed Distance**

**Discuss it**

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.

5/3 m/s | |

7/5 m/s | |

2/3 m/s | |

8/5 m/s |

**Time Speed Distance**

**Discuss it**

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.

69.4 km/h | |

78.6 km/h | |

87.5 km/h | |

40.5 km/h |

**Ratio and Proportion**

**Time Speed Distance**

**Discuss it**

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.

6 h 23 min | |

6 h 22 min | |

6 h 21 min | |

6 h 24 min |

**Time Speed Distance**

**Discuss it**

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.

11 km/h | |

12 km/h | |

13 km/h | |

15 km/h |

**Time Speed Distance**

**Discuss it**

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.

17 | |

15 | |

19 | |

20 |

**Time Speed Distance**

**Discuss it**

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?

20 | |

5 | |

10 | |

18 |

**Time Speed Distance**

**Discuss it**

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?

38.4 | |

100 | |

80.4 | |

160 |

**Time Speed Distance**

**Discuss it**

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.