Answer: The walking speed is 4.2 feet per second.
Step-by-step explanation:
If your walking speed is S, then we can use the relation:
Time = distance/speed.
in the moving sidewalk the speed is S + 1.8ft/s.
moving forward:
speed = S + 1.8ft/s
Distance = 100 feet
Time = T
T = 100ft/(S + 1.8ft/s)
moving in the opposite direction (now the velocity of the moving sidewalk must be subtracted)
speed = S - 1.8ft/s
distance = 40 feet
time = T
T = 40ft/(S - 1.8ft/s)
Then we have two equations:
T = 100ft/(S + 1.8ft/s)
T = 40ft/(S - 1.8ft/s)
We can replace T in the second equation by the expression in the first one:
100ft/(S + 1.8ft/s) = 40ft/(S - 1.8ft/s)
now we can solve it for S.
100ft*(S - 1.8ft/s) = 40ft*(S + 1.8ft/s)
100ft*S - (100ft*1.8ft/s) = 40ft*S + (40ft*1.8ft/s)
100ft*S - 40ft*S = (100ft*1.8ft/s)+ (40ft*1.8ft/s)
S*(100ft - 40ft) = S*60ft = (100ft*1.8ft/s)+ (40ft*1.8ft/s)
S = ( (100ft*1.8ft/s)+ (40ft*1.8ft/s) )/60ft = (252ft^2/s)/60ft = 4.2 ft/s
The walking speed is 4.2 feet per second.
