SOLUTION: a boat travels 1 km upstream and 1 km back. the time for the round trip is 9 hrs. the speed of the stream is 4 km/hr. what is the speed of the boat in still water?

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Question 1030818: a boat travels 1 km upstream and 1 km back. the time for the round trip is 9 hrs. the speed of the stream is 4 km/hr. what is the speed of the boat in still water?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
a boat travels 1 km upstream and 1 km back.
the time for the round trip is 9 hrs. the speed of the stream is 4 km/hr.
what is the speed of the boat in still water?
:
let s = speed in still water
then
(s-4) = effective speed upstream
and
(s+4) = effective speed downstream
:
write a time equation; time = dist/speed
:
Time up + time down = 9 hrs
+ = 9
multiply equation by (s-4)(s+4), cancel the denominators
(s+4) + (s-4) = 9(s-4)(s+4)
2s = 9(s^2 - 16)
2s = 9s - 144
A quadratic equation
0 = 9s^2 - 2s - 144
Using the quadratic formula a=9; b=-2; c=-144, I got a positive solution of
s = 4.11265 km/h is the speed in still water
:
:
Check this, find the actual time each way
1/8.11265 = .12326 hrs
1/.11265 = 8.87705 hrs
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total time: 9.00 hrs