SOLUTION: A motorboat, whose speed is 24 km/h in still water, takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream

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Question 943502: A motorboat, whose speed is 24 km/h in still water, takes 1 hour more to
go 32 km upstream than to return downstream to the same spot. Find the
speed of the stream
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A motorboat, whose speed is 24 km/h in still water, takes 1 hour more to
go 32 km upstream than to return downstream to the same spot.
Find the speed of the stream
:
let c = the rate of the stream current
then
(24+c) = the effective speed of the boat downstream
and
(24-c) = the effective speed up stream
:
Write a time equation; time = dist/rate
:
Time up - time down = 1 hr
32%2F%28%2824-c%29%29 - 32%2F%28%2824%2Bc%29%29 = 1
Multiply by (24-c)(24+c)
(24-c)(24+c)*32%2F%28%2824-c%29%29 - (24-c)(24+c)*32%2F%28%2824%2Bc%29%29 = 1(24-x)(24+c)
Cancel the denominators
32(24+c) - 32(24-c) = (24-c)(24+c)
768 + 32c - 768 + 32c = 576 + 24c - 24c - c^2
Combine like terms
64c = 576 - c^2
Arrange as a quadratic equation
c^2 + 64c - 576 = 0
You can use the quadratic formula a=1, b=64, c=-576, but this will factor to:
(x+72)(x-8) = 0
The positive solution is all we want here
x = 8 km/hr is the rate of the current
:
:
See if that checks out, find the actual time each way
Effective speeds: 16 upstream; 32 down stream
32/16 = 2 hrs
32/32 = 1 hr
-------------
differ: 1 hr