<PRE><B>Question 525096</B>
At the airport, Cheryl and Bill are walking to the gate (at the same speed) to catch their flight to Las Vegas.
 Since Bill wants a window seat, he steps onto the moving sidewalk and continues to walk while Cheryl uses the stationary walkway.
 If the sidewalk moves at 1 mps and Bill saves 50 seconds covering the 300-meter distance, what is their walking speed.
:
Let w = normal walking speed mps
then
(w+1) = speed on the moving walkway
:
Write a time equation; time = dist/speed
:
normal time - walkway time = 50 sec
{{{300/w}}} - {{{300/((w+1))}}} = 50
multiply by w(w+1), results
300(w+1) - 300w = 50w(w+1)
300w + 300 - 300w = 50w^2 + 50w
A quadratic equation
0 = 50w^2 + 50w - 300
simplify, divide by 50
w^2 + w - 6 = 0
Factors to
(w+3)(w-2) = 0
the positive solution
w = 2 mps, normal walking speed
:
:
Check this by finding the actual time of each walker
300/2 = 150 sec
300/3 = 100 sec
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differ: 50 sec, confirms our solution
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