SOLUTION: A motor boat went downstream for 120 km and immediately returned. It took the boat 15 hours to complete the round trip. If the speed of the river was twice as high, the trip downst

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Question 730627: A motor boat went downstream for 120 km and immediately returned. It took the boat 15 hours to complete the round trip. If the speed of the river was twice as high, the trip downstream and back would have taken 24 hours. What is the speed of the boat in still water?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
speed of boat = x
speed of current = y
120%2F%28x%2By%29+%2B120%2F%28x-y%29=+15...................(1)
120%28x-y%29%2B120%28x%2By%29+=+15%28x%5E2-y%5E2%29
120x-120y%2B120x%2B120y=15%28x%5E2-y%5E2%29
240x=15%28x%5E2-y%5E2%29

120%2F%28x%2B2y%29+%2B120%2F%28x-2y%29+=+24....................(2)
240x=24%28x%5E2-4y%5E2%29
15%28x%5E2-y%5E2%29=24%28x%5E2-4y%5E2%29
-9x%5E2=-81y%5E2
x/y =3,
x=3y
120%2F%28x%2By%29+%2B120%2F%28x-y%29=+15
substitute x=3y
120%2F%284y%29+%2B120%2F%282y%29=15
120+240=60y
360=60y
y=6 kphthe speed of current
x= 3y
x= 18kph speed of boat