   SEARCH HOME Math Central Quandaries & Queries  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 (b + c) = b + c miles

On the return trip the boat travels at (b - c) miles per hour and hence

20 = 2.5 (b - c) = 2.5 b - 2.5 c miles

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     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.