D=RT WORD Problem

Question

A patrol boat travels eleven hours on a trip downstream with a six-mph current. The return trip against the same current takes fourteen hours. Find the speed of the boat in still water.

Answer 1

D = distance (mile) = rate (mph) x time (hr)

 

Let R = boat speed in still water (mph)

     C = current speed = 6 mph

     t1 = 11 hr = time boat travels distance D with current C

     t2 = 14 hr = time boat travels distance D against current C

 

 with current:     D = (R + C)*t1

 

against current:  D = (R - C)*t2

 

Set D's equal and solve for R:

 

(R + 6)*11 = (R - 6)*14

 

11*R + 66 = 14*R - 84

 

3*R = 150

 

R = 150/3 = 50 mph in still water