Question 248643
The current in a stream moves at a speed of 3mph. A boat travels 45mi upstream and 45 mi downstream in a total time of 8 hours. What is the speed of the boat in still water?

Distance traveled = speed(rate) * time traveled or D = R*T

Let X be the speed of the boat in still water.
Let T be the time taken to go upstream.
Then 8-T is the time taken to go downstream.

We then have two equations in two unknowns as follows:

(1.) (X-3)*T = 45
(2.) (X+3)*(8-T) = 45

Solve the first equation for T. 

T=45/(X-3)

Substitute this value for T in the second equation:

(X+3)*(8-T)
(X+3)*(8-(45/(X-3)) = 45

Expand:

(8*X)-(45*X/(X-3)) + 24 - 135/((X-3) = 45

Multiply both sides by (X-3):

(8*X)*(X-3) - 45*X + 24*(X-3) - 135 = 45*(X-3)

Expand:

8*X^2 - 24*X -45*X + 24*X - 72 - 135 = 45*X - 135

Simplify:

8*X^2 -90*X - 72 = 0

Divide both sides by 2:

4*X^2 - 45*X - 36 = 0

Factor:

(4X+3) * (X-12) = 0

Solve for Positive X.