SOLUTION: Two three year olds, Adam and Louis, are riding their super speeders tricycles back and forth across a playground. Both of them ride at a constant speed (although their speeds are

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Question 447146: Two three year olds, Adam and Louis, are riding their super speeders tricycles back and forth across a playground. Both of them ride at a constant speed (although their speeds are not equal to each other), and they each take no time to turn around at either end of the playground. Adam starts at the west end and louis starts at the east end. they start at the same time and ride toward each other. They meet and pass each other 30 feet from the east end of the playground. When they reach the opposite end of the playground, they turn and ride back toward each other. They meet again 14 feet from the west end of the playground. What is the length of the playground?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Both of them ride at a constant speed (although their speeds are not equal to
each other), and they each take no time to turn around at either end of the playground.
Adam starts at the west end and louis starts at the east end.
they start at the same time and ride toward each other.
They meet and pass each other 30 feet from the east end of the playground.
When they reach the opposite end of the playground, they turn and ride back toward each other.
They meet again 14 feet from the west end of the playground.
What is the length of the playground?
:
Let d = distance across the playground
:
First meeting:
L travels 30'
A travels (d-30)
:
Second meeting
L travels: (d-30) + 14 = (d-16)
A travels: 30 + (d-14) = (d+16)
:
The relationship of the distance each traveled remains the same.
Ratio L:A
30%2F%28%28d-30%29%29 = %28%28d-16%29%29%2F%28%28d%2B16%29%29
Cross multiply
30(d+16) = (d-30)(d-16)
30d + 480 = d^2 - 16d - 30d + 480
Combine like term on the right
0 = d^2 - 16d - 30d - 30d + 480 - 480
which is
d^2 - 76d = 0
factor out d
d(d - 76) = 0
Two solution
d = 0
and
d = 76 ft is the length of the playground
:
:
Confirm this relationship
30%2F%28%2876-30%29%29 = %28%2876-16%29%29%2F%28%2876%2B16%29%29
30%2F46 = %28%2860%29%29%2F%28%2892%29%29
.652 = .652