TIME DISTANCE SET 7

Q.1 There are 2 cars moving in opposite directions. the distance between them is 300cm. They move forward for 100cm with a speed of 50 cm/s, and comes back 50 cms at 25cm/s. After how many seconds will the cars collide?

A) 10 seconds

B) 11 seconds

C) 12 seconds

D) 13 seconds

Ans. C

12 seconds — first 50cms 4 sec then 50 cms 4 sec and so…on

Q.2 There is a 50m long army platoon marching ahead. The last person in the platoon wants to give a letter to the first person leading the platoon. So while the platoon is marching he runs ahead, reaches the first person and hands over the letter to him and without stopping he runs and comes back to his original position. In the mean time the whole platoon has moved ahead by 50m.
The question is how much distance did the last person cover in that time. Assuming that he ran the whole distance with uniform speed.

A) 120.71 meters

B) 120.61 meters

C) 121.71 meters

D) 121.61 meters

Ans. A

It is given that the platoon and the last person moved with uniform speed. Also, they both moved for the identical amount of time. Hence, the ratio of the distance they covered – while person moving forward and backword – are equal.
Let’s assume that when the last person reached the first person, the platoon moved X meters forward.
Thus, while moving forward the last person moved (50+X) meters whereas the platoon moved X meters.
Similarly, while moving back the last person moved [50-(50-X)] X meters whereas the platoon moved (50-X) meters.
Now, as the ratios are equal,
(50+X)/X = X/(50-X)
(50+X)*(50-X) = X*X
Solving, X=35.355 meters
Thus, total distance covered by the last person
= (50+X) + X
= 2*X + 50
= 2*(35.355) + 50
= 120.71 meters
Note that at first glance, one might think that the total distance covered by the last person is 100 meters, as he ran the total length of the platoon (50 meters) twice. true, but that’s the relative distance covered by the last person i.e. assuming that the platoon is stationary.

Q.3 A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There is a bus for every half an hour interval. The car starts at 12 noon. Each bus travels at a speed of 25 km/hr. Distance between A and B is 100 km. During its journey , The number of buses that the car encounter is

A) 14

B) 15

C) 16

D) 17

Ans. D

A——————- B
Bus Car
25km/hr 20 km/hr
6:00 AM 12:00 noon
Therefore, Speed of bus = 25/6

& Speed of car = 20/12 = 5/3

Thus, S bus + SCar = 25/6 + 5/3 = 35/6

Therefore, Distance is given i.e. = 100 km

Therefore, distance/Speed i.e. 100 * 6 / 3 5 = 17

Q.4 One-third of a journey was covered at a rate of 25 km per hour, one-fourth at the rate of 30 km per hour and the rest at the rate of 50 km per hour. Find the average speed of the whole journey.
A) 33 1/3 km/h
B) 66 1/3 km/h
C) 36 1/6 km/h
D) 63 1/3 km/h
Ans. A

Let the total distance of the journey be 12 km
Distance covered at the speed of 25 km/h = 4 km
Distance covered at the speed of 30 km/h = 3 km
Distance covered at the speed of 50 km/h = 5 km
Average speed = = = 33 km/h

Q.5 A Formula One driver covers some distance at the speed of 60 mph. With what speed should he return so that his average speed of the total journey comes out to be 120 mph?
A) 180 mph
B) 120 mph
C) 150 mph
D) Not possible
Ans. D