SOLUTION: The question is: A river has a current of 3mph. A boat goes 35 miles upstream in the same time as it goes 45 miles downstream. Find the speed of the boat in still water? I tried

Question 455372: The question is: A river has a current of 3mph. A boat goes 35 miles upstream in the same time as it goes 45 miles downstream. Find the speed of the boat in still water?
I tried the following: d=rt let upstream = u and downstream =d so
45=3u+d - (35=3u+d) Please help i don't believe I'm doing this correctly.

Found 2 solutions by stanbon, oberobic:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The question is: A river has a current of 3mph. A boat goes 35 miles upstream in the same time as it goes 45 miles downstream. Find the speed of the boat in still water?
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downstream rate = b+3 mph where "b" is boat speed in still water
upstream rate = b-3 mph where "b" is boat speed in still water
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Upstream DATA:
distance = 35 miles ; rate = b-3 mph ; time = d/r = 35/(b-3) hrs.
---------------
Dosnstream DATA:
distance = 45 miles ; rate = b+3 mph ; time = d/r = 45/(b+3)
------------------
Equation:
time up = time down
35/(b-3) = 45/(b+3)
---
35b + 105 = 45b - 135
---
10b = 240
---
b = 24 mph (speed of the boat in still water)
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Cheers,
Stan H.
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Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Going upstream:
d = rt
r = speed of boat in still water - 3 mph current
d = 35 (given)
35 = (s-3)*t
Going downstream:
d = rt
r = speed of boat in still water + 3 mph current
d = 45 (given)
45 = (s+3)*t
We also are told t is the same for both trips.
But we are not told what t is.
So, we can turn the equations around to be in the form: t =
Then since t = t, we can solve.
.
35/(s-3) = t
45/(s+3) = t
So,
35/(s-3) = 45/(s+3)
Cross multiply
35*(s+3) = 45*(s-3)
35s + 105 = 45s - 135
Subtract 35s from both sides
105 = 10s -135
Add 135 to both sides
240 = 10s
10s = 240
Divide both sides by 10
s = 24
.
Always check your answers!
In this case, if you plug s=24 into the equations, will the t's be equal?
35/(24-3) = 35/21 = 5/3
45/(24+3) = 45/27 = 5/3
Yes!
.
So the speed of the boat in still water is 24 mph.
.
Done.
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