M46-14

Question

A railway employee is standing on a platform and observes two trains traveling in opposite directions on parallel tracks. He observes that the first train takes 40 seconds to completely pass the employee (from the moment the locomotive reaches him until the last carriage clears him), while the second takes 25 seconds to completely pass him. If the two trains take 30 seconds to completely pass each other (from the moment the fronts meet to the moment the rears separate), what is the ratio of the speed of the slower train to that of the faster train?

A. 1:4
B. 1:3
C. 1:2
D. 2:3
E. 3:4

A. 1:4
B. 1:3
C. 1:2
D. 2:3
E. 3:4

Bunuel · Answer

Official Solution:

A railway employee is standing on a platform and observes two trains traveling in opposite directions on parallel tracks. He observes that the first train takes 40 seconds to completely pass the employee (from the moment the locomotive reaches him until the last carriage clears him), while the second takes 25 seconds to completely pass him. If the two trains take 30 seconds to completely pass each other (from the moment the fronts meet to the moment the rears separate), what is the ratio of the speed of the slower train to that of the faster train?

A. 1:4
B. 1:3
C. 1:2
D. 2:3
E. 3:4

A. 1:4
B. 1:3
C. 1:2
D. 2:3
E. 3:4

This question can be solved in several ways. Below is arguably the most straightforward and reliable approach.
 
Let L1 and L2 be the lengths, and S1 and S2 the speeds, of the first and second trains, respectively.
 
The first train takes 40 seconds to pass the employee, so its length is:
 
L1 = S1 * 40
 
The second train takes 25 seconds to pass the employee, so its length is:
 
L2 = S2 * 25
 
When the two trains pass each other, they cover the total distance L1 + L2 in 30 seconds at a combined speed of S1 + S2.
 
So, we have the equation:
 
L1 + L2 = (S1 + S2) * 30
 
Substitute the expressions for L1 and L2:
 
S1 * 40 + S2 * 25 = (S1 + S2) * 30
 
10 * S1 = 5 * S2
 
S1 : S2 = 5 : 10 = 1 : 2

Answer: C

omnisvitae · Answer

I like the solution - it’s helpful.

LoyalMeter · Answer

I like the solution - it’s helpful.

Anshulyadavvv · Answer

Hello, unrelated to the question but from the information that they cross each other in 30 sec, can we conclude that first train is longer and slower, and second train is faster and shorter. 
My logic is that since the time taken by 1st is 40sec which is higher than 30sec (the relative time taken) by 10 sec, and similary, time by 2nd train is lower by 5 seconds to the relative time; it must mean that besides being slower the first train is also longer. Basically it covered a longer distance than train 2 hence taking more time. If the difference was same, we can say they are the same length. Am I correct in making this conclusion?

M46-14

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