Question

A moving sidewalk at an airport glides a rate of 1.8 feet per second. Walking on the moving sidewalk, you travel 100 feet forward in the same time it takes to travel 40 feet in the opposite direction. Find your walking speed on a nonmoving sidewalk.

Answer 1

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.