Question

An airport terminal has a moving sidewalk to speed passengers through a long corridor. Larry does not use the moving sidewalk; he takes 145 s to walk through the corridor. Curly, who simply stands on the moving sidewalk, covers the same distance in 85 s. Moe boards the sidewalk and walks along it. How long does Moe take to move through the corridor? Assume that Larry and Moe walk at the same speed.

Answer 1

@austinL Let the distance covered by the sidewalk is x meters
so speed of Larry
\[\frac{x}{145} m/s\]
Do you get this?

Answer 2

I did indeed.

Answer 3

Can you find the speed of moving side walk?

Answer 4

Should be x/85 m/s right? Because that is how long it took Curly.

Answer 5

Correct, now Moe walks on the sidewalk with Larry's walking speed.
But he's also on the side walk, so what should be his total speed?

Answer 6

Would it be Larry and Curly's added together?

Answer 7

yes, so how much time he will take to cover the distance x meters?

Answer 8

Im drawing a blank.

Answer 9

230x/12325 m/s?

Answer 10

Yeah that's the speed, time would be
\[\frac{x}{\frac{230x} {12325}} seconds\]
can you simplify and find the time?

Answer 11

Would it be 53.59 seconds?

Answer 12

Correct :)

Answer 13

Very cool, thank you very much for your help!

Answer 14

Welcome !

Answer 15

let the distance to cover is d.
walking velocity of Moe = walking velocity of larry = d/145
velocity of side walk = velocity of Curly = d/85

hence net velocity of Moe = walking velocity of Moe + velocity of sidewalk
= d/145 + d/85

hence time taken by Moe = distance to be covered / velocity
= d/(d/145 + d/85)
= \[1/(1/145 + 1/85)\]
= 85*145/(85 + 145)
= 53.6 seconds