Question

C. A river cruise boat sailed 120 miles down the Mississippi River for six hours. It took eighthours to return. Find the rate of the cruise boat in still water and the rate of the current.

Answer 1

Let:

x = Speed of the boat downstream

y = Speed of the boat upstream

A river cruise boat sailed 120 miles down the Mississippi River for six hours. So:

$\begin{gathered} 6(x+y)=120 \\ x+y=\frac{120}{6} \\ x+y=20_{\text{ }}(1) \end{gathered}$

It took eight hours to return. So:

$\begin{gathered} 8(x-y)=120 \\ x-y=\frac{120}{8} \\ x-y=15_{\text{ }}(2) \end{gathered}$

Using elimination method:

$\begin{gathered} (1)+(2) \\ x+x+y-y=20+15 \\ 2x=35 \\ x=\frac{35}{2} \\ x=17.5 \end{gathered}$

Replace x into (2):

$\begin{gathered} 17.5-y=15 \\ y=17.5-15 \\ y=2.5 \end{gathered}$

Therefore, the rate of the cruise boat in still water is 17.5 mph and the rate of the current is 2.5mph