Algebra Word Problem

Question

A motorboat maintained a constant speed of 14 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 16 minutes; the return trip takes 12 minutes. What is the speed of the current?

Answer 1

This is still just an application of Rate * Time = Distance.

 

Let x = the speed of the current

 

                        Rate      Time          Distance

      Upstream    14-x      16/60         16/60(14-x)

      Downstream  14+x   12/60          12/60(14+x)

 

Since the distances of the trips must be the same, we get (reducing fractions)

 

4/15(14-x) = 3/15(14+x)

56/15-4/15 x = 42/15 + 3/15x       multiply by 15 to eliminate all the denominators

56-4x = 42 + 3x

14      =     7x

2 = x.

 

So the speed of the current is 2 miles per hour.