Excluding stoppages, the speed of a bus is 54km/hr and including stoppage, it is 45km/hr. For how many minutes does the

BTGModeratorVI wrote: ↑

Wed Dec 16, 2020 12:45 pm

Excluding stoppages, the speed of a bus is 54km/hr and including stoppage, it is 45km/hr. For how many minutes does the bus stop per hour?

(A) 9
(B) 10
(C) 12
(D) 15
(E) 20

Answer: B
Source: 800 score

The average speed (including stoppage) is 45 km/hr
Distance = (rate)(time)
So, in ONE hour, the distance traveled = (45)(1) = 45 km

The average speed (excluding stoppage) is 54 km/hr
At this speed, HOW long will it take the bus travel 45 km?
time = distance/rate
So, time = 45/54
= 5/6 hours
= 50 minutes

At a speed of 54 km/hr, the bus can travel 45 km every 50 minutes.
So, it must be motionless for the other 10 minutes.

Answer: B

BTGModeratorVI wrote: ↑

Wed Dec 16, 2020 12:45 pm

Excluding stoppages, the speed of a bus is 54km/hr and including stoppage, it is 45km/hr. For how many minutes does the bus stop per hour?

(A) 9
(B) 10
(C) 12
(D) 15
(E) 20

Answer: B

Solution:


Let the total distance the bus travels be d. Let the bus travel for t hours in total and stop for s hours in total. Notice that the speed of the bus is d/t excluding stoppage and d/(t + s) including stoppage. Setting the first expression equal to 54, we obtain:

d/t = 54

Similarly, setting the second expression equal to 45, we obtain:

d/(t + s) = 45

Let’s rewrite the first equation as d = 54t and substitute this expression for d in the second equation:

54t/(t + s) = 45

54t = 45(t + s)

54t = 45t + 45s

9t = 45s

t = 5s

Now, notice that the ratio of the time the bus stops to the total travel time is s/(t + s). Substituting t = 5s, we see that the bus spends s/(5s + s) = s/6s = 1/6 of every hour stopping, which is equivalent to 60 * 1/6 = 10 minutes of stopping each hour.

Answer: B