Without stoppages a train travels a certain distance with an

thank you, your method is really good, just need to strike at right time.

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

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

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

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

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

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.

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.

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.

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

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

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

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

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)

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

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

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.