Llewyn takes 45 minutes to drive his boat upstream from the dock to his favorite fishing spot. It takes him 30 minutes to drive the boat back downstream to the dock. The boat’s speed going downstream is four miles per hour faster than its speed going upstream. Find the boat’s upstream and downstream speeds.

Llewyn takes 45 minutes to drive his boat upstream

It takes him 30 minutes to drive the boat back downstream to the dock.

The boat’s speed going downstream is 4 miles per hour faster than its speed going upstream.

Let Boat's Uphill be r.

Then,Boat's downhill will be $=r+4$

We write the speeds in the chart.

The speed is in miles per hour, so we need to express the times in hours, too, in order for the units to be the same.

Remember, one hour is 60 minutes. So:

45 minutesrole="math" localid="1647261257908" $\frac{45}{60}=\frac{3}{4}hours$

30 minutes $\frac{30}{60}=\frac{1}{2}hours$

Next, we multiply rate times time to fill in the distance column.

Distance travelled by uphill is equals to distance travelled by downhill

$$\begin{gathered} \frac{3}{4}r=\frac{1}{2}(4+r) \\ 3r=2(4+r) \\ 3r=8+2r \\ 3r-2r=8 \\ r=8 \\ r+4=8+4 \\ =12 \end{gathered}$$

Boat's Uphill$8mph$

Boat's Downhill$12mph$