An airport conveyor belt is 120 meters long, and moves at a constant

Question

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

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

KarishmaB · Accepted Answer

You need no variables here.

For half the time the man is standing still. So he is moving at a speed of 2 m/s.
For the other half, the man is moving walking and the belt is moving so his effective speed is 2 + 4 = 6 m/s
So his average speed = (2 + 6)/2 = 4 m/s (Avg speed is the avg of two speeds when time taken is equal)

Time taken = Distance/Avg speed = 120/4 = 30 sec

EMPOWERgmatRichC · Answer

Hi All,

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

pushpitkc · Answer

Total length of the conveyor belt : 120 meters.
When the conveyor belt is running for half of the time, 
the man is also walking and the conveyor belt is running.
The effective speed is the speed of the man + speed of the belt = 4+2 = 6m/s

Total time taken to cross the conveyor belt is 2x
For half the time he is stationary on the conveyor belt 
and other half he is walking on the conveyor belt,
Therefore
6x + 2x = 120
8x = 120 => x = 15

Hence the total time taken to cross the conveyor belt is 2x :  30seconds(Option B)

gracie · Answer

let d=distance man moves while standing
if standing and walking time are equal, then d/2=(120-d)/6
d=30 meters
(30/2)+(90/6)=30 seconds total time to cross entire conveyor belt
B

ehsan090 · Answer

pushpitkc 
why total time taken is 2x
TIA

shivam2506 · Answer

ehsan090

You can take total time as x also. In that case the equation becomes: 6*(x/2) + 2*(x/2) = 120.
On sloving you will get x=30.

Mahmud6 · Answer

When TIME traveled in each segment is constant, then average speed is simple mean of speeds. 
So, Average Speed is (2+6)/2=4 mps

Therefor, time taken would be 
Distance/Avg speed = 120/4 = 30 seconds.

rnn · Answer

hi, i need some help - I know the answer is incorrect, I am trying to understand the flaw in my logic. i was trying to think about it this way:

if the person had walked on the belt throughout the 120m then it would have taken him 20 seconds. 6 = 120/t => t = 20. The problem states that half the time he stands still so out of 20 seconds, he walked only for 10 seconds. Thus he covered 60m while walking (6 = d/10) => 60m.

The other 60m he didnt walk so it took him 30 seconds (2/60/t) => t = 30.

Therefore total time is 30+10 = 40

Can someone let me know where I went wrong? Thanks

EMPOWERgmatRichC · Answer

Hi nausherwan,

If you review your work, you should be able to spot the error: your calculation shows a 40-second timeframe, but the person walks for 10 seconds and stands for 30 seconds.... that is NOT a person who walks for HALF of the time (here it's 10/40 = 1/4 of the time).

There are a couple of different ways to approach this question; my approach (a few posts up form your post) uses the answers to our advantage.

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

rnn · Answer

Thanks a lot Rich...

ScottTargetTestPrep · Answer

If he walks but does not use the conveyor belt, it will take him 120/4 = 30 seconds to walk the length of the conveyor belt.

Therefore, he walks for 15 seconds on the conveyor belt before he stops and lets the conveyor belt move at its own speed.

For the 15 seconds he walks on the conveyor belt, he’s moving 4 + 2 = 6 m/s.

Therefore, he moves 6 x 15 = 90 meters on the conveyor belt while he is walking on it.

For the remaining 30 meters that he is not walking, it takes 30/2 = 15 seconds.

Therefore, it takes a total of 15 + 15 = 30 seconds to move from one end of the conveyor belt to the other.

Alternate Solution:

Let’s keep in mind that the rate of the man is 2 + 4 = 6 m/s when he is walking on the conveyor belt and 2 m/s when he is standing still. In the light of this information, let’s test each answer choice.

A) 25 seconds

If the entire trip took 25 seconds, he walks 12.5 seconds on the conveyor belt and stands still for another 12.5 seconds. Therefore, he covers a distance of (12.5)*6 + (12.5)*2 = 75 + 25 = 100 meters. Answer choice A is not correct.

B) 30 seconds

If the entire trip took 30 seconds, he walks 15 seconds on the conveyor belt and stands still for another 15 seconds. Therefore, he covers a distance of (15)*6 + (15)*2 = 90 + 30 = 120 meters. Answer choice B is correct.

Answer: B

andreagonzalez2k · Answer

Let be 't' the time it takes him to cross the conveyor.

2*\frac{t}{2}+(2+4)*\frac{t}{2}=120

t+3t=120

4t=120

t=30

Answer B

Vetrick · Answer

Though the method followed by the some of the experts take less time than the method I am going to write here, this method is one another way to solve.

There are two speeds the man travels at while on the conveyor belt - 6 & 2. They are in the ratio 3:1. Therefore distance travelled on the conveyor belt is also in the same ratio (speed is proportional to distance).

So, the distance travelled at 6 m/s is 90 and the distance travelled at 2 m/s is 30.

Total time = 90/6 + 30/2 = 15 + 15 = 30 s

bumpbot · Answer

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An airport conveyor belt is 120 meters long, and moves at a constant

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