SOLUTION: A river has a current speed of 5 miles per hour. A boat travels down river for 20 miles. It then makes the return trip up the river. If the return trip took 8 hours and 20 minutes

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Question 1159172: A river has a current speed of 5 miles per hour. A boat travels down river for 20 miles. It then makes the return trip up the river. If the return trip took 8 hours and 20 minutes longer than the trip down river, what is the speed of the boat in still water?
Found 4 solutions by josgarithmetic, MathTherapy, greenestamps, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
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r, speed of boat in still water

20%2F%28r-5%29-20%2F%28r%2B5%29=8%261%2F3--------solve for r.

Divide both sides by 5, multiply both sides by 3,
12%2F%28r-5%29-12%2F%28r%2B5%29=5
.
.
120=5r%5E2-125
-
24=r%5E2-25
24%2B25=r%5E2
49=r%5E2
highlight%28r=7%29




....
highlight%28r=%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

A river has a current speed of 5 miles per hour. A boat travels down river for 20 miles. It then makes the return trip up the river. If the return trip took 8 hours and 20 minutes longer than the trip down river, what is the speed of the boat in still water?
Correct answer: Speed of boat in still water: highlight_green%28matrix%281%2C2%2C+7%2C+mph%29%29

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


If r is the speed in mph of the boat in still water, then its upstream speed is r-5 and its downstream speed is r+5.

upstream time: 20/(r-5)
downstream time: 20/(r+5)

The upstream time is 8 1/3 hours (25/3 hours) greater than the downstream time:

20%2F%28r-5%29+=+20%2F%28r%2B5%29%2B25%2F3
Multiply everything by the least common denominator, 3(r-5)(r+5):

60%28r%2B5%29+=+60%28r-5%29%2B25%28r%5E2-25%29
60r%2B300+=+60r-300%2B25r%5E2-625
1225+=+25r%5E2
r%5E2+=+49
r+=+7 (clearly the r = -7 solution makes no sense...)

ANSWER: The speed of the boat in still water is 7mph

CHECK:
upstream speed: 20/(7-5) = 20/2 = 10
downstream speed: 20/(7+5) = 20/12 = 5/3 = 1 2/3
10 - 1 2/3 = 8 1/3

Answer by ikleyn(52776) About Me  (Show Source):