SOLUTION: 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?

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?
Found 2 solutions by checkley77, dabanfield:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
D=RT OT T=D/R
8=45*2/R
8=45/(R+3)+45/(R-3)
8=(45R-135+45R+135)/(R+3)(R-3)
8=(90R)/(R^2-9)
8(R^2-9)=90R
8R^2-72-90R=0
8R^2-90R-72=0
(2R-24)(4+3)=0
2R-24=0
2R=24
R=12 MPH. IS THE SPEED OF THE BOAT.
PROOF:
8=45/(12+3)+45/(12-3)
8=45/15+45/9
8=3+5
8=8

Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
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.

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