SOLUTION: The speed of a boat in still water is 10mph. It travels 15 miles upstream and 15 downstream in a total of 4 hours. what is the speed of the current?

Question 220956: The speed of a boat in still water is 10mph. It travels 15 miles upstream and 15 downstream in a total of 4 hours. what is the speed of the current?
Found 2 solutions by checkley77, MathTherapy:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
D=RT
(15+15)=[(10-X)*(10+X)]4
30=[100-X^2]4
30=400-4X^2
4X^2=400-30
4X^2=370
X^2=370/4
X^2=92.5
X=SQRT92.5
X=9.617 MPH FOR THE CURRENT.
PROOF:
(15+15)=[(10-9.617)+(10+9.617)]4
30=[.383*19.617)4
30=7.51.4*4
30=30

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
The speed of a boat in still water is 10mph. It travels 15 miles upstream and 15 downstream in a total of 4 hours. what is the speed of the current?

Let speed of current = C

Since speed in still water is 10 mph, then the speed to go upstream, against the current = 10 - C, and the speed downstream, with the current = 10 + C

Now, since total trip took 4 hours to travel in both directions of 15 miles each, and since Time = , then we'll have:

15(10 + C) + 15(10 - C) = 4 * (10 - C)(10 + C) ----- Multiplying by LCD (10 - C)(10 + C), in order to get rid of denominators

mph

Therefore, speed of current = mph
----------
Check
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Time upstream: or hours

Time downstream: or hour

Total time: (3 + 1) = 4 hours

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