SOLUTION: The moving sidewalk at Chicago's O'Hare airport moves 1.8 ft/sec. Walking on the moving sidewalk, Camille travels 105 ft forward in the time it takes to travel 51 ft in the opposit

Algebra ->  Expressions-with-variables -> SOLUTION: The moving sidewalk at Chicago's O'Hare airport moves 1.8 ft/sec. Walking on the moving sidewalk, Camille travels 105 ft forward in the time it takes to travel 51 ft in the opposit      Log On


   

Question 187612: The moving sidewalk at Chicago's O'Hare airport moves 1.8 ft/sec. Walking on the moving sidewalk, Camille travels 105 ft forward in the time it takes to travel 51 ft in the opposite direction. How fast would Camille be walking on a non-moving sidewalk?
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The moving sidewalk at Chicago's O'Hare airport moves 1.8 ft/sec.
Walking on the moving sidewalk, Camille travels 105 ft forward in the time it takes to travel 51 ft in the opposite direction.
How fast would Camille be walking on a non-moving sidewalk?
---
Let that rate be "r.
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Forward DATA:
time = x seconds : distance = 105 ft ; rate = 105/x ft/sec
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Backward DATA:
time = x seconds ; distance = 51 ft ; rate = 51/x ft/sec
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Equations
r + 1.8 = 105/x
r - 1.8 = 51/x
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2r = 54/x
r = 27/x
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Substitute to solve for "x":
27/x + 1.8 = 105/x
78/x = 1.8
x = 78/1.8 =
x = 43.3333
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Substitute into r = 27/x to solve for "r":
r = 27/43.3333
r = 0.6231 ft.sec(Camille's rate on a non-moving walkway)
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Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The moving sidewalk at Chicago's O'Hare airport moves 1.8 ft/sec.
Walking on the moving sidewalk, Camille travels 105 ft forward in the
time it takes to travel 51 ft in the opposite direction.
How fast would Camille be walking on a non-moving sidewalk?
:
Let x = C's speed on a non-moving sidewalk
then
(x-1.8) = speed against the sidewalk movement
and
(x+1.8) = speed with the sidewalk movement
;
Write a time equation time = dist%2Fspeed
Time with = time against
105%2F%28%28x%2B1.8%29%29 = 51%2F%28%28x-1.8%29%29
cross multiply
105(x-1.8) = 51(x+1.8)
105x - 189 = 51x + 91.8
105x - 51x = 91.8 + 189
54x = 280.8
x = 280.8%2F54
x = 5.2 ft/sec is C's sidewalk speed
:
:
Check solution by finding the times:
105/7 = 15 sec
51/3.4 = 15 sec