SOLUTION: Bob can row 9 mph in still water. The total time to travel downstream and return upstream to the starting point is 3 hours and 0 minutes. If the total distance downstream and back

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Question 1027546: Bob can row 9 mph in still water. The total time to travel downstream and return upstream to the starting point is 3 hours and 0 minutes. If the total distance downstream and back is 24 miles, determine the speed of the river (current speed).
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Bob can row 9 mph in still water.
The total time to travel downstream and return upstream to the starting point is 3 hours and 0 minutes.
If the total distance downstream and back is 24 miles, determine the speed of the river (current speed).
:
let c = the speed of the current
then
(9+c) = effective speed downstream
and
(9-c) = effective speed up-stream
:
Write a time equation; time = dist/speed
That's 12 mi one-way.
:
Time down + time up = 3 hrs
12%2F%289%2Bc%29 + 12%2F%289-c%29 = 3
multiply equation by (9+c)(9-c)
(9+c)(9-c)*12%2F%289%2Bc%29 + (9+c)(9-c)*12%2F%289-c%29 = 3(9+c)(9-c)
Cancel the denominators, FOIL the right side
12(9-c) + 12(9+c) = 3(81 - c^2)
108 - 12c + 108 + 12c = 243 - 3c^2
216 = 243 - 3c^2
3c^2 = 243 - 216
3c^2 = 27
c^2 = 27/3
c^2 = 9
c = sqrt%289%29
c = 3 mph is the current
:
:
See if that checks out, find the actual time each way
effective speed are 12 mph and 6 mph
12/12 = 1 hr
12/6 = 2 hr
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total: 3 hrs