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by nidhis.1408 » Tue Oct 16, 2012 9:16 am
Barry walks from one end to the other of a 30-meter long moving walkway at a constant rate in 30 seconds, assisted by the walkway. When he reaches the end, he reverses direction and continues walking with the same speed, but this time it takes him 120 seconds because he is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take Barry to walk from one end of the walkway to the other?


a. 48
b. 60
c. 72
d. 75
e. 80
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by anuprajan5 » Tue Oct 16, 2012 9:31 am
Distance - 30m

This is like a boat upstream /downstream problem

Time taken to go with the walkway = 30 sec
Time taken to go against the walkway = 120 sec

Lets taken Barry's speed as a and the walkway's speed as b

Speed with the walkway = a+b
Speed against the walkway = a-b

The idea is to find Barry's speed ie: a and calculate how long it would take if we did not hace the effect of b - the walkway's speed

Speed = Distance/Time

a+b = 30/30
a-b = 30/120

You can solve both to find a = 5/8 and b = 3/8

[spoiler]now we have a, 30 = 5/8*t

t = 48 sec. Answer A[/spoiler]
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by GMATGuruNY » Tue Oct 16, 2012 6:40 pm
nidhis.1408 wrote:Barry walks from one end to the other of a 30-meter long moving walkway at a constant rate in 30 seconds, assisted by the walkway. When he reaches the end, he reverses direction and continues walking with the same speed, but this time it takes him 120 seconds because he is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take Barry to walk from one end of the walkway to the other?


a. 48
b. 60
c. 72
d. 75
e. 80
We can plug in the answers, which represent Barry's time when the walkway is not moving.
To make the math easy, we should start with 60, a nice round value.

Answer choice B: 60 seconds
Barry's rate = d/t = 30/60 = 1/2 meter per second.
Since the time when Barry is ASSISTED by the walkway is 30 seconds, the combined rate for Barry and the moving walkway = d/r = 30/30 = 1 meter per second.
Thus, the walkway's rate = (combined rate for Barry and the moving walkway) - (Barry's rate) = 1 - 1/2 = 1/2 meter per second.
Thus, when Barry walks AGAINST the direction of the moving walkway, the rate of travel = (Barry's rate) - (walkway's rate) = 1/2 - 1/2 = 0 meters per second.
Doesn't work.
When Barry travels AGAINST the direction of the moving walkway, his rate must be GREATER than the walkway's rate; otherwise, he won't move.
Since Barry's rate needs to INCREASE, his time when the walkway is not moving must DECREASE.

The correct answer is A.
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