Relative Motion Help Needed!?

Question

Here's the question:

A man runs as fast as he can along a moving sidewalk from one end to the other, taking 2.50 s. A security agent appears, and the man runs as fast as he can back along the sidewalk to his starting point, taking 10.00 s. What is the ratio of the man's running speed to the sidewalk's speed.

I'd like have more than just the answer, I need to know how to work the problem.

Thanks for any assistance I get! It's much appreciated.

Answer 1

r=running speed
s=sidewalk speed
d=length of walk
r+s=d/2.5
r-s=d/10
2r=d/2.5+d/10
2s=d/2.5-d/10
r/s= {1/2.5+1/10}/{1/2.5-1/10}=5/3