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The speed of a moving walkway is typically about 2.5 feet per second.
Walking on such a moving walkway, it takes Judy a total of 40 seconds to travel
50 feet with the movement of the walkway and then back against the movement of the walkway.
What is Judy's normal walking speed?
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Let x be the Judy' normal speed, in ft/s.
Then Judy' speed with the walkway is x+2.5 ft/s,
and against the walkway it is x-2.5 ft/s.
Write and use the time equation
+ = 40 seconds (1)
for the total trip.
To solve, multiply both sides by (x-2.5)*(x+2.5) = x^2 - 6.25. You will get
50(x-2.5) + 50*(x+2.5) = 40(x^2 -6.25),
100x = 40x^2 - 250,
40x^2 - 100x - 250 = 0,
4x^2 - 10x - 25 = 0,
x = = = .
We want the positive root and deny the negative one
x = = 4.045085 ft/s (rounded).
CHECK equation (1): = 40.0 seconds,
which convinces me that the solution is good.
ANSWER. The Judy' walking speed is about 4.05 ft/s.
Solved.