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# D01-25

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Math Expert
Joined: 02 Sep 2009
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Math Expert
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General Discussion
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No hours stopped from A to B = 3 hrs
No hours stopped from B to A = 5 hrs (10*0.5)
No hours stopped at B = 1 hour

Let Distance be D
Speed traveled by train from A to B = x
Speed traveled by train from B to A = 2x
3+(D/X)=5+(D/2x) (given)
D = 4x ------------------(1)

Total time = Time taken from AtoB + Time taken from BtoA + hours stopped in B
Total time = 3+(D/x) + 5+(D/2x) + 1
Sub (1) in above

total time = 15hrs Option (B)
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I think this is a high-quality question and I agree with explanation.
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ALTERNATIVE SOLUTION for those who are not able to fully understand Bunuel's approach.

Make a grid as per the given data

Rate..................Time........Distance.......... Stops(hrs)
A to B r..............1/r.................1..............3
B to A 2r............1/2r ..............1.............. 5

It is given that the time it took for both trips is the same.
Use algebra to set up the equation

TOTAL TIME for A to B = TOTAL Time for B to A
1/r + 3 = 1/2r + 5
r=1/4

Substitute r=1/4 in equations for total time for round trip.

Time for ROUNDTRIP = Total time for A to B + Total time for B to A + 1 hour stop at B
1/r + 3 + 1/2r + 5 + 1
7 + 7 + 1

Total time for roundtrip = 15hours.

If the above solution helped you. Hit Kudos like a Hero
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Bunuel wrote:
A train is traveling at a constant speed from city A to city B. Along this trip the train makes three one-hour stops and reaches city B. At city B the train is stopped again for 1 hour. After that the train makes the return trip from city B to city A at a constant speed which is twice the speed of the first trip. Along this return trip the train makes ten thirty minutes stops and reaches city A. If both trips took the same amount of time, how many hours was the roundtrip?

A. 14
B. 15
C. 16
D. 17
E. 18

Stoppage Time from A to B = 3*60 mins = 180 mins = 3 hrs
Stoppage Time from B to A = 10*30 mins = 300 mins = 5 hrs
Since both trips took same time, it means trip from A to B took 120 mins extra.

Since speeds in the two trips are in the ratio 1:2, travel time taken would be in the ratio 2:1. The difference of 1 is actually 120 mins so total travel time = 3*120 = 360 mins = 6 hrs

Total Time for Return Trip = Total travel time + Stoppage Time + Break Time at B = 6 hrs+ 8 hrs + 1 hr = 15 hrs

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I think this is a high-quality question and I agree with explanation.
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Let’s assume two variables for the unknown quantities viz distance between A and B and the speed of the train.
Let distance between A and B = d miles.
Let speed of train = d miles per hour.

Then, total time taken by train for onward journey = $$\frac{d }{ s}$$ + 3, taking into account the three one hour stops made on the way.

Total time taken by train for return journey = $$\frac{d }{ 2s}$$ + 5 because the train travelled at twice the speed and also took 300 minutes i.e. 5 hours of stops.

Since both trips took the same amount of time,$$\frac{ d}{s} + 3 = \frac{d}{2s} + 5$$. Solving the equation, we get d = 4s.

Therefore, time taken for onward journey = $$\frac{4s}{s}$$ + 3 = 7 hours and,
Time taken for return journey = $$\frac{4s }{ 2s}$$ + 5 = 7 hours.
The train also stopped for 1 hour at B.

Therefore, total time taken for the round trip = 7 + 7 + 1 = 15 hours.
The correct answer option is B.

Hope that helps!
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Joined: 07 Mar 2020
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If this this helps:-

Total time for completion of trip = $$t1+3+t2+5+1$$ = $$t1+t2+9$$ [t1-time travelled with speed r from A to B, t2-time travelled with speed 2r from B to A, +3 stoppage time from A to B, +5 is stoppage time from B to A , and +1 is extra stoppage at station B]. -----(3)
We know distance from A to B is same as B to A so We get $$r*t1=2r*t2$$=$$t1=2*t2$$. ------- (1)
Also given total time from A to B is same as time from B to A i.e $$t1+3=t2+5$$ ------ (2).

From (1) and (2) , We get $$t1=4,t2=2$$.
On putting t1 and t2 in (3) , We get total time as $$4+3+2+5+1=15$$.
Math Expert
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
Manager
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I used an alternate solution.

The statement states that the ratio of the speed for onward journey to the speed for return journey = 1:2
Hence time for the same ratio = 2:1
Further, lets assume the time the train is moving(without stoppages) for onward journey = t. Therefore the time the train is moving for return journey = t/2.

Therefore, t+3=t/2+5. t=4.
Total time = t+3+5+t/2+1(stop at B) = 4+9+2 = 15.
Option B.
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