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by sl750 » Sun Sep 04, 2011 2:47 am
A train is traveling at a constant speed and after making three one-hour stops reaches its destination. After waiting an hour it makes a return journey stopping a total of ten times, thirty minutes each but traveling at twice the speed. 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

Why is this equation wrong
S-speed; T-Time

S*(T+3)=2S(T+5) ? The question states that the amount of time traveled both ways is the same. I know that I get a negative answer for the time here, but I don't know why the equation is incorrect.

Also the answer given is 15. By following the explanation given, I arrived at 17. Any help is appreciated, Thanks
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by knight247 » Sun Sep 04, 2011 6:42 am
The thing with your equation is that you have included T as the travel time ONLY. The travel time on both the journeys is definitely not the same, as the duration of the stops is different. If on a 6 hr journey I halt for three hours then my actual travel time is 3 hrs. Similarly on a 6 hr journey I halt for 1 hr then my actual travel time is 5 hrs. So you can't have the same variable representing the actual travel times on both journeys.

Now,
For the 1st trip
Speed=s1
Distance=D
Time=D/s1
However, this is only the actual travel time. There was a 3 hr stop midway. So total time is
Total Duration=(D/s1)+3

For return trip,
Speed=2s1
Distance=d
Time=D/2s1
Again, there were 10 halts of 30 minutes each. So 10*30/60=5 hrs
So Total Duration=(D/2s1)+5

Now both these two are equal so,
(D/s1)+3=(D/2s1)+5
(D/s1)-(D/2s1)=2
(2D/2s1)-(D/2s1)=2
D/2s1=2
D/s1=4
Meaning, actual travel time for the 1st trip was 4 hrs. Plus the 3 hr halt.Total time =7 hrs
For the return trip, the actual travel time was 2 hrs. Plus the 5 hr halt.Total time=7 hrs
14hrs plus the 1 hr halt=15 hrs hence B
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