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Excluding stoppages, the speed of a bus is 54km/hr and including stopp

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Excluding stoppages, the speed of a bus is 54km/hr and including stopp  [#permalink]

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New post Updated on: 15 Mar 2019, 02:35
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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

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Originally posted by stonecold on 07 Apr 2017, 08:38.
Last edited by Bunuel on 15 Mar 2019, 02:35, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Excluding stoppages, the speed of a bus is 54km/hr and including stopp  [#permalink]

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New post 07 Apr 2017, 09:23
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stonecold wrote:
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)20
E)15


Great question.

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:

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Re: Excluding stoppages, the speed of a bus is 54km/hr and including stopp  [#permalink]

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New post 07 Apr 2017, 09:07
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We are given that speed of the Bus with stoppage is 45km/hr. Which means the Bus actually travels 45 km in an hour. This does not mean the bus actually travelled for full 60 minutes, because it is given that the bus had stoppages.

Now the duration in an hour the bus actually travels, the speed of the bus during that duration is 54km/hr.

So let's say the bus actually travels for T minutes in an hour. From the given information we can say

54 * T/60 = 45
T = 45 *60/54 = 50 minutes.

So the duration of the stoppage in 1 hour = 60 - 50 = 10 mins.

Answer is B)10
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Re: Excluding stoppages, the speed of a bus is 54km/hr and including stopp  [#permalink]

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New post 07 Apr 2017, 09:48
stonecold wrote:
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)20
E)15


let m=minutes per hour train is not stopped
45/54=m/60
m=50
60-50=10 minutes per hour train is stopped
B
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Re: Excluding stoppages, the speed of a bus is 54km/hr and including stopp  [#permalink]

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New post 09 Apr 2017, 00:16
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The point to note is that the bus TRAVELS at 54 mph, never at 45 mph; due to stoppages, the total time for the trip increases resulting in the reduction of AVERAGE speed to 45.
With stoppages, the bus travels 9 miles (54-45) less in 1 hr so the bus remains motionless for the span of time it would have taken to travel 9 miles which is 9/54=1/6 hrs=10 mins. Answer: B
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Re: Excluding stoppages, the speed of a bus is 54km/hr and including stopp  [#permalink]

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New post 10 Aug 2018, 14:07
Let's simplify it.. it took me a while to understand what the question wants (decode the question)... it's a little confusing..
in 1 hr, for how much time does the train stop?
fine.. so the train is actually travelling @ 45 km/hr (average) .. it includes stoppages too (Rest + Motion or R + M) and 45 km --> 1 hr which is why we choose 45 km... (first note).. secondly.. 54 km => Motion so, for 45 km (-> 1 hr) the train is in motion for 5/6 hrs => in 1 hr (-> 45 minutes) the train stops for 1/6 hrs = 10 minutes. simple..
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Re: Excluding stoppages, the speed of a bus is 54km/hr and including stopp   [#permalink] 10 Aug 2018, 14:07
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