Question 308152: A child is running on a moving sidewalk in an airport. When she runs against the sidewalk's motion, she travels 66ft in 11 seconds. When she runs with the sidewalk's motion, she travels 110ft in the same amount of time. What is the rate of the child on a still sidewalk and what is the rate of the moving sidewalk?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A child is running on a moving sidewalk in an airport.
When she runs against the sidewalk's motion, she travels 66ft in 11 seconds.
When she runs with the sidewalk's motion, she travels 110ft in the same amount of time.
What is the rate of the child on a still sidewalk and what is the rate of the moving sidewalk?
:
Let r = child's rate on a still sidewalk (ft/sec)
Let w = walkway speed
then
(r-w) = rate against
(r+w) = rate with
:
Write two distance equations; dist = time * rate
11(r-w) = 66
11(r+w) =110
:
Simplify both equations, divide both sides by 11, results:
r - w = 6
r + w = 10
---------------Adding eliminates w, find r
2r = 16
r = 8 ft/sec child's rate on a still sidewalk
:
Find w
8 + w = 10
w = 10 - 8
w = 2 ft/sec, rate of the side walk
;
:
Check solutions in original equations
11(8-2) = 66
11(8+2) = 110
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