# Time & Distance (13)

1. A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office?
1. 3 km
2. 4 km
3. 5 km
4. 6 km

Explanation :-

Average Speed = 2(S1 * S2)/(S1 + S2)
Here,  S1 = 3 km/h    &     S2 = 2 km/h
Average Speed = (2 * 3 * 2 ) / ( 3 + 2 ) = 12/5 km/h
Time = 5 hours
Distance Covered = (12/5) * 5 = 12 km
Therefore , Distance between his house and office = 12/2 = 6 km

2. A man rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. What is his average speed for the entire trip approximately?
1. 11.2 kmph
2. 10 kmph
3. 10.2 kmph
4. 10.8 kmph

Explanation :-

Total Distance = 10 +12 = 22 km
Time taken to cover 10 km with speed 12 km/h = 10/12 = 5/6 hrs
Time taken to cover 12 km with speed 10 km/h = 12/10 = 6/5 hrs
Total time = (5/6) + (6/5) = (25 + 36) / 30 = 61/30 hours
Average speed = Total Distance / Total Time = 22 / (61/30) = 660 / 61 = 10.8 km/ hour

3. An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in (1 &  2/3) hours, it must travel at a speed of:
1. 660 km/hr
2. 680 km/hr
3. 700 km/hr
4. 720 km/hr

Explanation :-

Distance = Speed * Time = (240 x 5) = 1200 km.
For distance = 1200 km   &    Time = (1 &  2/3)hrs =  5/3 hrs
Speed = 1200 /(5/3) = 720 km/hr

4. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. What is the speed of the car?
1. 80 kmph
2. 102 kmph
3. 120 kmph
4. 140 kmph

Explanation :-

Lets assume the speed of car = x km/h.
Therefore, the speed of train = (3/2)x km/h = 1.5 km/h
Distance covered = 75 (same for both car and train)
Time taken by the car to cover 75 km = 75/x
Time taken by the train to cover 75 km = 75/1.5x
Difference in times = 12.5 minutes.
(75/x) – (75/1.5x) = (125/10×60)
x = 120

5. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the flight ?
1. 2 hour
2. 112 hour
3. 12 hour
4. 1 hour

Explanation :-

Assume the duration of the flight be x hours.
Therefore , Original Speed = 600/x
Speed due to bad weather = 600/ (x + 1/2)
(600/x) – [ 600/ (x + 1/2)] = 200
(600/x) – [ 1200/ (2x + 1)] = 200
x (2x +1) = 3
2x^2 + x – 3 = 0
(2x + 3) (x – 1) = 0
x = -3/2   &   x = 1
By neglecting negative value of x , x = 1