SOLUTION: A boat goes 15 miles downstream. The return trip upstream takes 40 minutes longer. The boat can travel 12 miles per hour in still water. What is the speed of the current?

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Question 242521: A boat goes 15 miles downstream. The return trip upstream takes 40 minutes longer. The boat can travel 12 miles per hour in still water. What is the speed of the current?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A boat goes 15 miles downstream. The return trip upstream takes 40 minutes longer.
The boat can travel 12 miles per hour in still water.
What is the speed of the current?
:
let c = speed of the current
then
(12-c) = speed upstream
and
(12+c) = speed down stream
:
Change 40 min to 2%2F3 hr
:
Write a time equation; time = dist/speed
:
Time upstream - time down stream = 40 min
15%2F%28%2812-c%29%29 - 15%2F%28%2812%2Bc%29%29 = 2%2F3
Multiply equation by 3(12+c)(12-c); results
:
3(12+c)*15 - 3(12-c)*15 = 2(12-c)(12+c)
:
45(12+c) - 45(12-c) = 2(144 - c^2)
:
540 + 45c - 540 + 45c = 288 - 2c^2
Group like terms on the left
2c^2 + 45c + 45c + 540 - 540 - 288 = 0
which is
2c^2 + 90c - 288 = 0
Simplify, divide by 2
c^2 + 45c - 144 = 0
Factors to
(c+48)(c-3) = 0
positive solution
c = 3 mph is the current
:
:
Check solution:
15/9 - 15/15 =
5/3 - 3/3 = 2/3