Without stoppages a train travels a certain distance with an

Question

Without stoppages a train travels a certain distance with an average speed of 80 kmph and with stoppages it covers the same distance with an average speed of 60 kmph. What is the time in minutes per hour for which train stops?

A. 15 min/hr
B. 10 min/hr
C. 20 min/hr
D. 25 min/hr
E. None

@Bunuel , how can this be solved?

A. 15 min/hr
B. 10 min/hr
C. 20 min/hr
D. 25 min/hr
E. None

Zehnze · Accepted Answer

A much faster way is to determine how long it would take this train to travel 60 km at 80 km/h. 6/8 = 3/4 = 45 minutes of an hour, this means the train travels for 45 minutes to travel that distance and thus rests for 15 minutes. Just solved this problem in ~ 20 seconds with this method which is well below the 1 minute time constraint.

email2vm · Answer

sol:

80t = 60 (t+s)

t= usual time
S= stop time
t=3s

question wants us to find how much time per hour

t+s= 1 hr
4s= 60 min
s= 15 min

Bunuel · Answer

There are many ways to solve this question; however, arguably the least error-prone method is to assume a specific distance traveled. Let's say the distance traveled was 240 kilometers (the least common multiple of 80 and 60). This would mean that without the stoppage, the distance was covered in  \frac{240}{80} = 3  hours. With the stoppage, it would take  \frac{240}{60} = 4  hours. Thus, the stoppage was 1 hour out of 4, which makes 1/4 of an hour per hour, or 15 minutes per hour.

Answer: A.

gurpreetsingh · Answer

Let the distance be 240, t1 = 240/80 = 3 hours
t2 = 240/60 = 4 hours

difference in time = (4-3) = 1 but this is per 4 hours.

so the difference per hour is 1/4 which is 15 mins/hour....

jlgdr · Answer

Pick a smart number for the distance. lets say LCM 240 Without = 240/80 = 3 hours With = 240/60= 4 hours So in a trip of 4 hours, 1 hour is spent in stoppages Hence, 60/4 = 15 min/hr on stoppages Hope its clear Cheers! J

sanket1991 · Answer

1) there is a difference of 20kmph = 1/4th of 80kmph
2) that means train stops for 1/4th of an hour = 15 m/hr

gracie · Answer

Without stoppages a train travels a certain distance with an average speed of 80 kmph and with stoppages it covers the same distance with an average speed of 60 kmph. What is the time in minutes per hour for which train stops?

A. 15 min/hr
B. 10 min/hr
C. 20 min/hr
D. 25 min/hr
E. None

@Bunuel , how can this be solved?

A. 15 min/hr
B. 10 min/hr
C. 20 min/hr
D. 25 min/hr
E. None

let distance=80 k
stopping train's running time at 80 kmph=1 hour
let s=stopping time
80 k/(1+s) hr=60 kmph
s=1/3 hours
total time=1+1/3=4/3 hr
(1/3)/(4/3) hrs=1/4=15 minutes per hr stopping time
A

goforgmat · Answer

the train is travelling 20 kms less an hour..
20kms it could have covered in 20/80=1/4th hour or 15 mins
hence the train stops for 15 mins evry hour.

SVaidyaraman · Answer

The average speed is reduced by 1/4 th. So actual time traveled per hour is reduced by 1/4th. So the train stops 15 min/hr.

phoenix128 · Answer

Actual speed of train = 80km/hr. On stopping this reduces to 60km/hr. That is it loses 20km worth of time. For traveling 20km the train takes 20/80 hrs = 15 minutes.

Abhishek009 · Answer

Using formula

Time = Diff of Speed/Speed with stoppage*60

Or, Time =  \frac{80 - 60}{80}*60

Or, Time = 15 Min/Hr
  
Thus, answer must be (A) 15

gracie · Answer

let distance=80 k
80 k/80 kph=1 hr running time
80 k/60 kph=4/3 hr total time
1:4/3=3/4 ratio of running time to total time
thus, ratio of stopping time to total time=1/4
60 min/4=15 min
15 min/hr
A

Garimachaudhary · Answer

Here is a short trick or formula for this type of questions 
Time= difference in speed/speed without stoppage
So from the question
Difference in speed=80-60=20
Speed without stoppage =80
Put the value
T= 20/80= 1/4 hr
Now 1/4*60
=15 min/hr

Posted from my mobile device

carouselambra · Answer

Similar approach. 
The change in speed is (80-60)/80*100 = 25%
Hence, the speed decreased 1/4 times

This means that time would have increased by 4 times / hour
4/60 = 1/15

Fdambro294 · Answer

If the Train travels with NO Stops, the Average Speed = 80 kmph over this Distance.

In 1 hour----------------------->Train travels 80 km when it doesn't Stop

Then, the Train has several stops. The Average Speed over this Distance drops to 60 kmph (even though presumably the Train still travels at its Constant Rate when it is moving)

In 1 hour ----------------------> Train travels 60 km WITH Stops

Since the Usual Average Speed is 80 kmph over this Distance when the Train does not stop, each 1 hour the Train must be stopping 20 km.

If the train were not stopping, how quickly would the train cover this 20km that it does not get to cover? This Lost Time for Stops is the reason why the Average Speed over this Distance drops from 80 kmph to 60 kmph.

Time = (20 km of Distance Lost because of Stops) / (Constant Speed of 80 kmph) = 1/4 hour

So, over the course of 1 hour, the Train is NOT traveling 1/4 of that hour in order for the Average Speed to drop from 80 kmph to 60 kmph

15 minutes of every 1 hour the train is Stopping

(A)

Hoozan · Answer

Similar Question: https://gmatclub.com/forum/excluding-st ... 37716.html

KarishmaB · Answer

Check out my one minute solution to such a question by using weighted averages here: https://youtu.be/6Xjj5V2lxBg

kpop1234567890 · Answer

Number of stops/Number of speeding= 80-60/60-0
=20/60
=1/3

It means that in 60 min train stops for 1/4 and keeps going for 3/4. Hence 15 minute.

Solved by giving weights.

sanya511 · Answer

@Bunuel , how can this be solved?

Without stoppages a train travels a certain distance with an

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Without stoppages a train travels a certain distance with an

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards