Word Problem

Question

A motorboat can maintain a constant speed of 40 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 33 minutes; the return trip takes 22 minutes. What is the speed of the current?

Answer 1

speed of boat in still water = 40 mph

w = speed of stream

upstream time is 33 min = 33/60 hrs = 11/20 hrs

downstream time is 22 min = 22/60 hrs = 11/30 hours

 

The distance (d = vt) traveled either way is the same, but at different speeds and times.

 

Set upstream and downstream distances (vt) equal and solve for w.

 

(40 - w)(11/20) = (40 + w)(11/30)

 

(40 - w)/20 = (40 + w)/30

 

3(40 - w) = 2(40 + w)

 

120 - 3w = 80 + 2w

 

40 = 5w

 

w = 40/5 mph = 8 mph

 

Test the solution.