SOLUTION: 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 t

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Question 1208942: 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?

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
w, Judy's speed of walking
speed unit FEET PER SECONDS
50 feet each way travel distance
40 seconds total time of travel
RT=D OR D%2FR=T

50%2F%28w%2B2.5%29%2B50%2F%28w-2.5%29=40
Solve this for w.


Answer by ikleyn(52748) About Me  (Show Source):
You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~~ 

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

    50%2F%28x%2B2.5%29 + 50%2F%28x-2.5%29 = 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 = %2810+%2B-+sqrt%28%28-10%29%5E2-4%2A4%2A%28-25%29%29%29%2F%282%2A4%29 = %2810+%2B-+sqrt%28500%29%29%2F8 = %2810+%2B-+10%2Asqrt%285%29%29%2F8.


We want the positive root and deny the negative one

    x = %2810+%2B+10%2Asqrt%285%29%29%2F8 = 4.045085 ft/s  (rounded).


CHECK  equation  (1):   50%2F%284.045085%2B2.5%29+%2B+50%2F%284.045085-2.5%29 = 40.0 seconds, 

                        which convinces me that the solution is good.


ANSWER.  The Judy' walking speed is about 4.05 ft/s.

Solved.