Question

A suspicious-looking man runs as fast as he can along a moving sidewalk from one end to the other, taking 2.60 s. Then security agents appear and the man runs as fast as he can back along the sidewalk to his starting point, taking 11.9 s. What is the ratio of the man's running speed to the sidewalk's speed (running speed / sidewalk speed)?

Answer 1

1.56

Step-by-step explanation:

Let man run at constant speed =r m/s

Constant speed of side walk=s m/s

When the man running in the direction as the side walk is moving, then the relative speed =r+s m/s

When the man running in opposite direction as the side walk is moving=r-s m/s

Time taken when he run along a moving sidewalk from one end to the other=2.6 s

Time taken when he ran back along the side walk to his starting point=11.9 s

We have to find the ratio of the man's running speed to the side walk's speed.

Suppose the, length of sidewalk=d

Distance=
`speed* time`

`d=(r+s)* 2.6`

`d=(r-s)* 11.9`

`2.6r+2.6s=11.9r-11.9s`

`2.6s+11.9 s=11.9 r-2.6 r`

`14.5 s=9.3 r`

`(r)/(s)=(14.5)/(9.3)`

`(r)/(s)=1.56`