Asuspicious-looking man runs as fast as he can along a moving sidewalk from one end to the other, taking 2.20 s. then security agents appear and the man runs as fast as he can back along the sidewalk to his starting point, taking 10.3 s. what is the ratio of the man's running speed to the sidewalk's speed (running speed / sidewalk speed)?

The ratio is 1.54

Explanation:

Firs, we have to find the relative speed of the man moving forward and backward.

Forward:

vf = vs + vm

vm = the man's speed

vs = the sidewalk's speed

vf = relative velocity moving forward

Because we don't know how much the man moved,

vf = distance (meters) / time (seconds)

vf = x / 2.20s

Backward:

vb = -vm + vs

vb = relative velocity moving backward

vf = distance (meters) / time (seconds)

vf = -x / 10.30s

We now divide the relative speeds

vf / vb = (x / 2.20) / (-x / 10.30)

We cancel the x

vf / vb = -10.3s / 2.2s = -4.68

vf = -4.68 . vb

We now substitute this in the equation we used for the forward travel

-4.68vb = vm + vs

Subtracting this from the backward travel equation

vb - (-4.68vb) = -vm - vm + vs -vs

5.68vb = -2vm

vb = -2vm / 5.68

Now, adding to the backward travel equation

vb + (-4.68vb) = -vm + vm + vs + vs

-3.68vb = 2vs

Using the two resulting equations

-3.68 . (-2 / 5.68) vm = 2vs

7.36 / 5.68 vm = 2vs

vm / vs = 1.54

that would be because of both gravity and friction. so     c