# A motor boat , whose speed is 24 km/h in still water, takes 1 hr more to go 32 km upstream than to return downstream to the same spot, find the speed of the stream.

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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/(24-c)}-{32/(24+c)}=1

Multiply by (24-c)(24+c)

then we get an equation as:

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

since we want only positive part we get x=8

so the speed of the stream is 8km/h