Question

Translate to a system of equations and then solve: Jason paddled his canoe 24 miles upstream for 4 hours. It took him 3 hours to paddle back. Find the speed of the canoe in still water and the speed of the river current.

Short answer

the speed of the canoe in still water is 7 miles per hour

and the speed of the river current is 1 mile per hour

Step-by-step solution

Given Information 

Jason paddled his canoe 24 miles upstream for 4 hours. It took him 3 hours to paddle back

Assume variables and frame equations

Let 's' the speed of the canoe in still water and 'c' the speed of the river current.

Upstream :

Distance is 24 miles and time is 4 hours

speed is s-c

Distance = speed * time

$$\begin{gathered} 4(s-c)=24 \\ divideby4 \\ s-c=6 \end{gathered}$$

Downstream:

Distance is 24 miles and time is 3 hours

speed is s + c

$$\begin{gathered} 3(s+c)=24 \\ divideby3 \\ s+c=8 \end{gathered}$$

solve for s  and c

$$\begin{gathered} s-c=6 \\ s+c=8 \\ ----- \\ 2s=14 \\ divideby4 \\ s=7 \\ s-c=6 \\ 7-c=6 \\ -c=6-7 \\ -c=-1 \\ c=1 \end{gathered}$$

the speed of the canoe in still water is 7 miles per hour

and the speed of the river current is 1 mile per hour