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

Question

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

BrentGMATPrepNow · Accepted Answer

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:  B

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effatara · Answer

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

quantumliner · Answer

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

gracie · Answer

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

learner1234 · Answer

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..

Abhishek009 · Answer

Simple shortcut formula for approaching this question will be : Difference of speed / Speed without stoppage = 9/45*60 = 10, Answer must be (B)

Sumitgupta85 · Answer

It comes out to 12 mins according to your calculations.

Posted from my mobile device

ScottTargetTestPrep · Answer

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

Vishwas1998 · Answer

This question can be done using unitary method:

54-45=9 mins

mins=10mins

Hence, B

vineetpareek · Answer

54-45= 9 km less in 1 hour

Time taken to cover 9km with speed of 54km/hr

Time = distance/speed

9/54 =1/6 hr

=1/6 ×60 = 10 min

Posted from my mobile device

dendenden · Answer

Hi, I did the reverse where I made the distance = 54 km in 60 mins. then used this to calculate for the time if speed is 45 (54/45 = 6/5 hrs). I got 72 mins. So 72 - 60 = 12 mins.

Is there an error in my calculation hence why I didn't get the correct answer of 10 mins. or is this not a correct logical solution? I figured I would get the same answer when done in reverse but somehow I didn't..? Can someone help explain please? Thank you.

KarishmaB · Answer

dendenden Think about this - What you got is the time for which it stops in a period of 72 mins. What you actually need is the time for which it stops in a period of 60 mins. That brings you to an answer of 10 mins. Check out my one minute solution to such a question by using weighted averages here: https://youtu.be/6Xjj5V2lxBg

sanya511 · Answer

Bunuel , the approach this user used finds distance in 1 hour by multiplying 1 with the average speed, which is incorrect as you said  here . Can you please give the correct approach in solving this problem?

yogi.0195 · Answer

The bus covers 45 km in 1 hour, including stoppages. At 54 km/h (excluding stoppages), it would take 45⁄54 = 5⁄6 hour to cover 45 km. So, stoppage time is 1 − 5⁄6 = 1⁄6 hour, or 10 minutes. Hence, the bus stops 10 minutes every hour.

Bunuel · Answer

The solution calculates the stoppage time per 1 hour because the question specifically asks for the time the bus stops per hour.

He could have used a variable t instead of fixing the time to 1 hour, the result would have been the same in the end because the question is about the stoppage time in each hour.

Other solutions sometimes set the total time as t and solve for the stoppage proportionally, but since the question is already framed in terms of 1 hour, it’s fine to work directly with 1 hour as Brent did.

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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