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?

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) (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 hr
:
Write a time equation; time = dist/speed
:
Time upstream - time down stream = 40 min
- =
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

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