Speed of a current

Question

Suppose you paddle a row boat at a steady speed of 4 miles per hour. You go 6 miles downstream and then 6 miles upstream to get to where you started. The trip takes 4 hours. What is the speed of the current? Write an equation relating all the variables and use it to solve for the speed of the current. 

Answer 1

Begin with forming a table:

 

Direction           Rate (speed of boat + current)            Distance                   Time (distance/rate)

downstream       4+x                                                          6 miles                       6/(4+x)

upstream           4-x                                                           6 miles                       6/(4-x)

 

We know that the total time of the trip is 4 hours, so adding the two time components will give us this:

 

4= 6/(4+x) + 6/(4-x)

 

The least common denominator is (4+x)(4-x), you multiply both sides by that to get this:

 

4(4+x)(4-x)= 6(4-x) + 6(4+x)

 

4(16-x²)= 24 - 6x + 24- 6x   

 

Notice that the x will cancel out on the right side of the equation to get this:

 

4(16-x²)= 48

(16-x²)= 12

4 - x²= 0

4= x²

x= ±2 and for ease, x= 2

 

Next do a quick check to verify it is correct:

 

4= 6/(4+2) + 6/(4-2)

4= 6/6 + 6/2

4= 1 +3

4= 4