Suzy takes 50 minutes to hike uphill from the parking lot to the lookout tower. It takes her 30 minutes to hike back down to the parking lot. Her speed going downhill is 1.2 miles per hour faster than her speed going uphill. Find Suzy’s uphill and downhill speeds.

Letrbe the average speed

Suzy takes 50 minutes to hike uphill from the parking lot to the lookout tower.

It takes her 30 minutes to hike back down to the parking lot.

Her speed going downhill is 1.2 miles per hour faster than her speed going uphill.

Her speed walking and riding her bike. Let’s call her Uphill speed r.

Since her biking Downhill speed is 1.2 miles per hour faster, we will call that speed r + 1.2

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:

50 minutes $\frac{50}{60}=\frac{5}{6}hours$

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

$$\begin{gathered} \frac{5}{6}r=\frac{1}{2}(1.2+r) \\ 5r=3(1.2+r) \\ 5r=3.6+3r \\ 5r-3r=3.6 \\ 2r=3.6 \\ r=\frac{3.6}{2} \\ r=1.8 \\ r+1.2=1.8+1.2 \\ =2 \end{gathered}$$

Suzy's Uphill $r=1.8mph$

Suzy's Downhill$=2mph$