The average speed of a bus, excluding all stoppage time is 54 kmph and

Question

The average speed of a bus, excluding all stoppage time is 54 kmph and including all stoppage time is 45 kmph. Find the duration (in minutes) that the bus stops every hour.

A. 6 min 
B. 10 min 
C. 12 min 
D. 15 min 
E. 20 min

KarishmaB · Accepted Answer

I favour the logical approach though I will give an easier to follow approach too.
What is the diff between the two cases (excluding stoppage and including stoppage)? When you exclude stoppage, the total time taken does not include the stoppage time while calculating average speed. When you include stoppage, the total time taken includes stoppage time too when you calculate speed. The distance travelled in both cases is the same, just the time is different.

Logical approach:

If you travel non-stop, you cover 54 km in an hr so that's what your speedometer would show. 
When you include stoppage, you cover only 45 km in 1 hr. Why? You do not cover another 9 km because the time in which you would have covered this 9 km, you had stopped. If you had covered this 9 km at your regular speed (of 54 km/hr), you would have done it in 
9km/54 km/hr = 1/6 hr = 10 min

So for these 10 mins, you had stopped and hence your avg speed reduced.

Easier to follow approach:
Say distance covered in each case was 270 km.
Avg speed excluding stoppage = 270/54 = 5 hr
Time taken including stoppage = 270/45 = 6 hr

So in 6 hrs, 1 hr is stoppage time i.e. 1/6th is stoppage time i.e. 10 mins in 1 hr.

PTD1995 · Answer

Option B 
Let's say that for each hour, the bus will travel  x  minutes and stop  60-x  minutes.

We know that the  Av.Speed = 54 
Hence,

\frac{x*Av.Speed+(60-x)*0}{60}=45 
Leading to:  x=50

Thus, bus stops 10min every hour.

Abhishek009 · Answer

A simple shortcut formula exists for this problem -

Duration of stoppage is = Difference of Speed/Speed without Stoppage *60

Or, Duration of stoppage is =  \frac{( 54 - 45 )}{54 }*60

Or, Duration of stoppage is =  \frac{9}{54 }*60

Or, Duration of stoppage is =  \frac{1}{6 }*60

Or, Duration of stoppage is = 10  , Answer must be (B)

gracie · Answer

let s=stopping time
t=total time
54(t-s)=45t→
s/t=1/6 hour→
10 minutes stopping time per hour
B

ScottTargetTestPrep · Answer

We can let the distance be 45 km. Therefore, it takes the bus 45/54 = 5/6 hour = 50 minutes to travel this distance if there is no stoppage time. However, with stoppage time, it will take the bus 45/45 = 1 hour = 60 minutes to travel the same distance. Therefore, the stoppage time must be 60 - 50 = 10 minutes for every hour the bus travels.

Answer: B

ThatDudeKnows · Answer

If it doesn't stop at all, it covers 54km in an hour. Including stops, it covers 45km in an hour. That means it drove for 45/54 of the hour and was stopped for 9/54 of the hour. 9/54 of an our is 10 minutes.

Answer choice B.

TychoBrahe147 · Answer

t= time in movement, x= stoppage time, d= distance.
d is the same in both circumstances.
Formula avg speed= distance/time:
54= d/t
45= d/(t+x)
We are given t+x=60. Therefore, d=60*45
t = d/54 = 60*45/54 = 60*5/6 = 50
Substitute in t+x=60, we find x= 60-50=10
Answer B

Jaival · Answer

Hi can you help me by seeing if what I did is logically sound?
The distance is constant. and D=S/T
Case 1: D=54/t
Case 2: D=45/t+x
Equating both I get: 54 t+ 54x=45t
9t=-54x
t=-6x
And as t=1hour=60minutes
60=-6x
x=-10minutes

iamjatinagrawal · Answer

Excluding the halts, speed =54km/hr

Including the halts, speed =45km/hr

Simple method to solve such a question: ((Excluding the halts speed-Including the halts)/Excluding the halts)*minutes in an hour

Hence, the answer is  ((54−45)/54)*60=10 minutes.

pappal · Answer

since the question deals in average speeds, lets apply law of averages to solve it.
let us assume that bus stops x mins. per hour or x/60 hrs per hour 
or in other words we can also say that it runs for a time of 1-x/60=(60-x)/60 per hour.
by using law of averages
{54*(60-x)/60} + {0*x/60} =45 we use zero speed for this time since its stoppage time
solving this we can get x=10 mins

The average speed of a bus, excluding all stoppage time is 54 kmph and

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The average speed of a bus, excluding all stoppage time is 54 kmph and

Prep Toolkit

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