91Ó°ÊÓ

Consider the given question,

Distance traveled by the cruise boat is $80$miles.

Time taken by the cruise boat to travel downstream is $4$hours.

Time taken by the cruise boat to travel upstream is $5$hours.

Assume $x$to be the rate of the cruise boat in still water and$y$to be the rate of the current.

Consider the given question,

When the boat travels $80$miles downstream in $4$hours, then the current will help the cruise boat.

So, $$\begin{gathered} 4\left(x+y\right)=80 \\ x+y=20......\left(\mathrm{i}\right) \end{gathered}$$

When the travels $80$miles upstream in $5$hours, then the current will slow the cruise boat.

So,role="math" localid="1644340164407" $$\begin{gathered} 5\left(x-y\right)=80 \\ x-y=16......\left(\mathrm{ii}\right) \end{gathered}$$

Add equations (i) and (ii),

$$\begin{gathered} \left(x+y\right)+\left(x-y\right)=20+16 \\ 2x=36 \\ x=18 \end{gathered}$$

Substituting $x=18$in equation (i),

$$\begin{gathered} 18+y=20 \\ y=2 \end{gathered}$$

Substitute the values in equation (i),

$$\begin{gathered} 4\left(18+2\right)=80 \\ 4\left(20\right)=80 \\ 80=80 \end{gathered}$$

This is true.

Substitute the values in equation (ii),

$$\begin{gathered} 18-2=16 \\ 16=16 \end{gathered}$$

This is true.

The rate of the cruise boat in still water is $18$mph.

The rate of the current is$2$mph.