SOLUTION: two swimmers swim towards each other with constant velocity,they meet each other at 50 km from east ,turn around & go to their respective ends and meet again at 20km from west.what

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Question 752791: two swimmers swim towards each other with constant velocity,they meet each other at 50 km from east ,turn around & go to their respective ends and meet again at 20km from west.what is the total length of pool?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
You must mean meters not km here.
:
two swimmers swim towards each other with constant velocity,
they meet each other at 50 m from east, turn around & go to
their respective ends and meet again at 20 m from west.
what is the total length of pool?
:
Let x = the length of the pool
:
Their first meeting
1st swimmer travels 50 m east
2nd swimmer travels (x-50) m from the west
:
Their second meeting
1st swimmer travels (x-50) + 20 = (x-30)
2nd swimmer travels 50 + (x-20) = (x+30)
:
The ratio of the distances of the swimmers is the same for each scenario
50%2F%28%28x-50%29%29 = %28%28x-30%29%29%2F%28%28x%2B30%29%29
cross multiply
50(x+30) = (x-50)(x-30)
FOIL
50x + 1500 = x^2 - 30x - 50x + 1500
50x + 1500 = x^2 - 80x + 1500
subtract 1500 from both sides
50x = x^2 - 80x
0 = x^2 - 80x - 50x
x^2 - 130x = 0
x^2 = 130x
divide both sides by x
x = 130 meters is the length of the pool