SOLUTION: boat travels 135 miles upstream, then back, in 24 hours. Current is 3 mph. What is the boat's still speed?
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Question 214475: boat travels 135 miles upstream, then back, in 24 hours. Current is 3 mph. What is the boat's still speed?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Use distance = rate times time, or 
Describe the upstream trip. The upstream trip is against the current, so the actual rate of travel is the boat's still water speed (
) minus the current, so 
. We can say that the upstream trip took 
hours, giving us:
t)
Describe the downstream trip. The downstream trip is with the current, so the actual rate of travel is the boat's still water speed plus the current, so 
. If the upstream trip took hours and the entire trip took 24 hours, then the downstream trip must have taken 
hours, giving us:
(24 - t))
Solve the two equations for :
Now we have two expressions in both equal to , so set them equal to each other:
Apply the LCD of 
:
}{r^2 - 9}\ =\ \frac{24(r^2 - 9)}{r^2 - 9} - \frac{135(r - 3)}{r^2 - 9})
Combine everything on the left:
}{r^2 - 9} - \frac{24(r^2 - 9)}{r^2 - 9} + \frac{135(r - 3)}{r^2 - 9}\ =\ 0)
Combine the numerators:
Multiply both sides by the denominator, leaving you with a quadratic in . It is ugly, but it does factor.
Solve the quadratic for and exclude the negative root (the boat certainly doesn't go backwards in still water). The positive root is the boat's still water speed.
John
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