Answer: 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
