miles per hour 4 12

Question

A? boat's crew rowed
 9
miles? downstream, with the? current, in
1.5
hours. The return trip? upstream, against the? current, covered the same? distance, but took
3
hours. Find the? crew's rowing rate in still water and the rate of the current.


The? crew's rowing rate in still water is
______?mile(s) per hour.

Answer 1

Jessica,

 

This is a classic distance, rate, time question. Remember that d = rt. In this problem d = 9 miles, and the trip downstream (with the current) takes t = 1.5 hours, which the trip upstream (against the current) takes t = 3 hours.

 

Call the speed of the boat in still water x, and let the speed of the current be y. The rate downstream is x + y, and the rate upstream is x − y. Now, plug this information into the d = rt relationship to create two equations in x and y:

 

9 = 1.5(x + y)

9 = 3(x − y)

 

Simplify:

 

9 = 1.5x + 1.5y

9 = 3x − 3y.

 

I will solve for x and y using elimination. Let's first multiply the first equation on both sides by 2 so that the y-terms will add up to zero:

 

18 = 3x + 3y

9 = 3x − 3y

 

Add these equations together, then solve for x:

 

27 = 6x

x = 27/6 = 9/2 = 4.5 miles per hour

 

You can find y in a similar way, but also can plug in x = 4.5 into one of the original two equations and solve for it too.

 

Plug x = 4.5 into 9 = 1.5x + 1.5y, obtaining

 

9 = 1.5(4.5) + 1.5 y

9 = 6.75 + 1.5y

1.5y = 2.25

y = 2.25/1.5 = 1.5 miles per hour.

 

The answers are that the crew can row the boat 4.5 miles per hour in still water and the speed of the current is 1.5 miles per hour.