SOLUTION: A barge travels 63 miles upriver and 63 miles downriver in a toal time of 15 hours. the speed of the current is 4 mph. Find the speed of the barge in still water.

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Question 290001: A barge travels 63 miles upriver and 63 miles downriver in a toal time of 15 hours. the speed of the current is 4 mph. Find the speed of the barge in still water.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
Let's call the speed of the barge S.
Against the current,
1.%28S-4%29%2AT1=63
With the current,
2.%28S%2B4%29%2AT2=63
and we also know
T1%2BT2=15
From eq. 1 and 2,
T1=63%2F%28S-4%29
T2=63%2F%28S%2B4%29
Then,
63%2F%28S-4%29%2B63%2F%28S%2B4%29=15
63%28S%2B4%29%2B63%28S-4%29=15%28S%2B4%29%28S-4%29
63S%2B252%2B63S-252=15%28S%5E2-4S%2B4S-16%29
126S=15S%5E2-240
15S%5E2-126S-240=0
5S%5E2-42S-80=0
You can factor this equation.
%285S%2B8%29%28S-10%29=0
Two solutions,
5S%2B8=0
5S=-8
S=-8%2F5
.
.
.
S-10=0
S=10
Since we specified the direction of with and against the current, we assumed the barge speed was positive, so we only keep the positive result.
highlight%28S=10%29