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## An airport conveyor belt is 120 meters long. . .

This topic has 1 expert reply and 2 member replies

### Top Member

Vincen Legendary Member
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#### An airport conveyor belt is 120 meters long. . .

Wed Sep 20, 2017 7:56 am
An airport conveyor belt is 120 meters long, and moves at a constant rate of 2m/s. A man carrying two suitcases walks at a constant rate of 4m/s. How long will it take him to cross from one end of the conveyor belt to the other, if the man only walks for half the time he is on the conveyor belt?

A) 25 seconds
B) 30 seconds
C) 42 seconds
D) 45 seconds
E) 54 seconds

The OA is B.

Can anybody explain this PS question to me? If you could make a graph it would be better. Thank you.

pannalal Junior | Next Rank: 30 Posts
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Fri Sep 22, 2017 1:51 am
Arithmetic Solution:
If man is walking on conveyor belt, his speed is 6 m per second (4m + 2m) whereas if he just stands on the conveyor, his speed is 2 m per second. As the man walks for half the time on the conveyor belt, the average speed is 4 m per second. So, total time taken to cover 120 meters is 120/4 = 30 seconds. Answer (C)

pannalal Junior | Next Rank: 30 Posts
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Thu Sep 21, 2017 11:17 pm
If man is walking on conveyor belt, his speed is 6 m per second (4m + 2m) whereas if he just stands on the conveyor, his speed is 2 m per second. Assuming that he takes, total 'n' seconds. Then,

6n/2 + 2n/2 = 120
or 3n + n = 120
or 4n = 120
or n = 30.

Thus, answer is 30 seconds. So, the correct option is (B).

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Wed Sep 20, 2017 9:47 am
Hi Vincen,

While the prompt does not state it, we're meant to assume that the man is walking WITH the flow of the conveyor belt (meaning that he moves FASTER because he's walking AND the conveyor belt is moving him forward).

Thus, there are two speeds that the man moves at are :
2 meters/sec when he stands on the conveyor belt
6 meters/sec when he walks on the conveyor belt.

We're told that the conveyor belt is 120 meters long and that the man walks for half of the TIME that he's on the conveyor belt (NOT half of the distance). We're asked how much total time it takes the man to cross the 120 meters. This question can be solved by TESTing THE ANSWERS.

Let's TEST Answer B: 30 seconds.

Since he spends HALF the TIME walking and the other half standing, he would have traveled:
15 seconds @ 6 meters/sec = 90 meters
15 seconds @ 2 meters/sec = 30 meters
Total Distance = 90 + 30 = 120 meters
This is an exact match for what we were told, so this MUST be the answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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