Question 882551
The speed of a moving walkway is typically about 2.5 ft/sec.
 Walking on such a moving walkway, it takes Karen a total of 40 seconds to travel 50 ft with the movement of the walkway
 and then back again against the movement of the walkway. 
What is Karen's normal walking speed?
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Let w = the walking speed
then
(w+2.5) = effective speed going with the walkway
and
(s-2.5) = effective speed going against
:
Write a time equation; time = dist/speed
:
With time + against time = 40 sec
{{{50/((w+2.5))}}}  {{{50/((w-2.5))}}} = 40
multiply by (w+2.5)(w-2.5), cancel the denominators and you have
50(w-2.5) + 50(w+2.5) = 40(w+2.5)(w-2.5)
50w - 125 + 50w + 125 = 40(w^2 - 6.25)
100w = 40w - 250
A quadratic equation
0 = 40w^2 - 100w - 250
simplify, divide by 10
4w^2 - 10w - 25 = 0
Use the quadratic formula to find w, only positive solution will make sense
I got a positive solution of 4.045 ft/sec for K's walking speed
;
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You can check this out by finding the time each way should total 40 sec
50/(4.045+2.5) =
50/(4.045-2.5) =
:
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Did explain this it to you?  Let me know. ankor@att.net