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

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An airport conveyor belt is 120 meters long, and moves at a constant  [#permalink]

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New post 28 Jul 2017, 08:39
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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

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An airport conveyor belt is 120 meters long, and moves at a constant  [#permalink]

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New post 28 Jul 2017, 12:02
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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)
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An airport conveyor belt is 120 meters long, and moves at a constant  [#permalink]

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New post Updated on: 06 Dec 2017, 09:58
Bunuel wrote:
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


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

Originally posted by gracie on 28 Jul 2017, 12:50.
Last edited by gracie on 06 Dec 2017, 09:58, edited 2 times in total.
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Re: An airport conveyor belt is 120 meters long, and moves at a constant  [#permalink]

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New post 10 Aug 2017, 07:47
pushpitkc wrote:
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)


pushpitkc
why total time taken is 2x
TIA
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Re: An airport conveyor belt is 120 meters long, and moves at a constant  [#permalink]

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New post 10 Aug 2017, 08:53
ehsan090 wrote:
pushpitkc wrote:
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)


pushpitkc
why total time taken is 2x
TIA



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.
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Re: An airport conveyor belt is 120 meters long, and moves at a constant  [#permalink]

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New post 10 Aug 2017, 10:11
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Bunuel wrote:
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


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
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Re: An airport conveyor belt is 120 meters long, and moves at a constant  [#permalink]

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New post 05 Dec 2017, 13:15
1
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.

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Re: An airport conveyor belt is 120 meters long, and moves at a constant  [#permalink]

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New post 02 Feb 2018, 23:14
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.
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Re: An airport conveyor belt is 120 meters long, and moves at a constant &nbs [#permalink] 02 Feb 2018, 23:14
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