Word problem

Question

A motorboat heads upstream on a river that has a current of 3 mph The trip upstream takes five hours on the return trip takes 2.5 hours what is the speed of the motorboat.  Assume a motorboat maintains a constant speed relative to the water 

Answer 1

This is a variation on the standard rate/distance/time problem (D=R*T).  The distance in both directions is the same, the time is as noted in the problem, and the rate is different in each direction because of the current.  Let R=the speed of the boat.  Upstream the rate will be R-3, and the downstream rate is R+3.  Since the distance is the same we can write the equation as this:

 

(R-3)*5 = (R+3)*2.5  Solve this algebraically

 

5R-15 = 2.5R + 7.5

 

2.5R = 22.5

 

R = 9