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| Math Central | Quandaries & Queries |
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A boat on a river travels downstream between two points, 20 miles apart, in one hour. The return trip against the current takes 2 1/2 hours. What is the speed of the boat? The answer in the book says 14 mi/hr, but I don't understand how to figure it out. It must be very simple, but I'm stuck. -Sonja |
Hi Sonja,
Suppose that the speed of the boat in still water is b miles per hour and the speed of the current in the river is c miles per hour. Then for the trip downstream the boat travels at (b + c) miles per hour. Since distance = time 
rate we can conclude that
20 = 1
On the return trip the boat travels at (b - c) miles per hour and hence
20 = 2.5
Hence you have a pair of equations to solve
b + c = 20
2.5b - 2.5c = 20
Since you want b I would eliminate c by multiplying the first equation by 2.5 and add the two resulting equations.
I hope this helps,
Penny
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