SOLUTION: The speed of a stream is 4 mph. A boat travels 7 miles upstream in the same time it takes to travel 15 miles downstream. What is the speed of the boat in still water?

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Question 263127: The speed of a stream is 4 mph. A boat travels 7 miles upstream in the same time it takes to travel 15 miles downstream. What is the speed of the boat in still water?
Found 3 solutions by drk, stanbon, checkley77:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
This is an RTD question. Here is a table based on the given information:
up/down . . . . . . . . . . .rate . . . . . . . . . . .time . . . . . . . . . .distnace
upstream . . . . . . . . . . r-4 . . . . . . . . . . T . . . . . . . . . . . . . . 7
downstream . . . . . . . . r+4 . . . . . . . . . . T . . . . . . . . . . . . . . .15
Now, rate x time = distance, so
time = distance / rate.
solve each for T and we get
T = (7/(r-4))
T = (15/(r+4))
set the times equal and we get
7%2F%28r-4%29+=+15%2F%28r%2B4%29
cross multiply to get
7r+%2B+28+=+15r+-+60
subtract 7r to get
28+=+8r+-+60
add 60 to both sides to get
88+=+8r
divide by 8 to get
r+=+8

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The speed of a stream is 4 mph. A boat travels 7 miles upstream in the same time it takes to travel 15 miles downstream. What is the speed of the boat in still water?
-----
Upstream DATA:
distance = 7 miles ; rate = x-4 mph ; time = d/r = 7/(x-4) hrs.
----------------
Downstream DATA:
distance = 15 miles ; rate = x+4 mph ; time = 15/(x+4) hrs
--------------------------------------
Equation:
time = time
7/(x-4) = 15/(x+4)
7(x+4) = 15(x-4)
7x+28 = 15x-60
8x = 88
x = 11 mph (rate in still water)
====================================
Cheers,
Stan H.

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
D=RT OR T=D/R
TU=7/(R-C) TRAVEL UPSTREAM
TD=15/(R+C) TRAVEL DOWN STREAM.
THE TIMES ARE EQUAL.
7/(R-4)=15/(R+4) CROSS MULTIPLY.
15(R-4)=7(R+4)
15R-60=7R+28
15R-7R=28+60
8R=88
R=88/8
R=11 IS THE SPEED OF THE BOAT IN STILL WATER.
PROOF:
7/(11-4)=15(11+4)
7/7=15/15
1=1