algebra help

Question

A boat goes 360 miles downstream in the same time it can go 300 miles upstream. The speed of the current is 9 miles per hour. Find the speed of the boat in still water.

Answer 1

The key to problems of this kind is "DRT Chart:"

 

                                 D(mi)   R(mph)      T(hr)

Downstream                360        r+9          t

Ustream                       300       r-9            t

 

This chart summarizes the fact that Distance = Rate • Time, assuming travel time "t" same on both trips, and boat speeds (rate, w/o current 9 mph) "r".  Each line of the chart is an equation; your two equations are

 

360 = tr + 9t

300 = tr - 9t     Note that I did the distribution on the products RT.

 

Subtract 2nd equation from 1st...you get 60 = 9t and that gives t = 10/3 hours.

Plug that into one of the equations to solve for r.