SOLUTION: A woman rows a boat upstream from one point on a river to another point 4 miles away in one and a half hours. The return trip, traveling with the current, takes only 45 minutes. Ho

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Question 363734: A woman rows a boat upstream from one point on a river to another point 4 miles away in one and a half hours. The return trip, traveling with the current, takes only 45 minutes. How fast is the current flowing?
Found 2 solutions by stanbon, amoresroy:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A woman rows a boat upstream from one point on a river to another point 4 miles away in one and a half hours. The return trip, traveling with the current, takes only 45 minutes. How fast is the current flowing?
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Upstream DATA:
distance = 4 miles : time = 3/2 hr ; rate = d/t = 4/(3/2) = 8/3 mph
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Downstream DATA:
distance = 4 miles ; time = 3/4 hr ; rate = d/t = 4/(3/4) = 16/3 mph
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Equations:
b + c = 16/3 mph
b - c = 8/3 mph
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Subtract and solve for "c":
2c = 8/3
c = 4/3 mph (speed of the current)
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Cheers,
Stan H.
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Answer by amoresroy(361) (Show Source):
You can put this solution on YOUR website!
Distance = Speed * Time
Let s = speed of boat
c = speed of current
d s t
boat => 4 miles s-c 1 and 1/2 or 3/2
upstream
boat <=
downstream 4 miles s+c 45 mins or 3/4

We can now generate two equations.
4 = (s-c)*3/2
4 = (s+c)*3/4

Multiply 1st equation by 2/3

8/3 = s-c <= 1st new equation
Multiply 2nd equation by 4/3

16/3 = s+c <= 2nd new equation

Subtract the new 2nd equation by the new 1st equation
16/3 = s + c
- 8/3 = s - c
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8/3 = 0 + 2c
8/3 = 2c

Now divide both sides by 2.

4/3 = c

The speed of the current is 1 and 1/3 miles per hour.