SOLUTION: The current of a river is 4 miles per hour. A boat travels to a point 48 miles upstream and back in 5 hours. What is the speed of the boat in still water?
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Question 1055307: The current of a river is 4 miles per hour. A boat travels to a point 48 miles upstream and back in 5 hours. What is the speed of the boat in still water? Answer by ikleyn(52756) (Show Source):
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The current of a river is 4 miles per hour. A boat travels to a point 48 miles upstream and back in 5 hours. What is the speed of the boat in still water?
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Your equation is
= 5.
Here u is the unknown speed of the boat in still water.
The first addend in the left side is the time spent by the boat traveling upstream.
The second term is the time spent traveling downstream.
To solve equation (*), multiply both sides by (u-4)*(u+4). You will get
48(u+4) + 48(u-4) = 5(u^2-16), or
5u^2 - 96u - 80 = 0.
Solve using quadratic formula:
= = .
Disregard the negative root.
The solution is u = 20.
Answer. The boat speed in still water is 20 mph.
