Question

Two hot air balloons are traveling along the same path away from a town, beginning from different locations at the same time. Henry's balloon begins 15 miles from the town and is 31 miles from the town after 2 hours. The distance of Tasha's balloon from the town is represented by the function y= 5x + 25. Which balloon was farther from the town at the beginning, and which traveled more quickly?

Answer 1

Let's begin by listing out the information given to us:

a.

Henry:

$\begin{gathered} x=0;y=15miles \\ x=2hours;y=31miles \end{gathered}$

Tasha:

$\begin{gathered} y=5x+25 \\ \text{when time is 0 hours (at the beginning), we have:} \\ x=0 \\ y=5(0)+25=0+25=25miles \\ \text{when time is 2 hours, we have:} \\ x=2 \\ y=5(2)+25=10+25=35miles \end{gathered}$

As such, Tasha's balloon was farther from the town at the start than Henry's balloon (it was farther by 10 miles)

b.

After 2 hours, their balloon had travelled this far:

$\begin{gathered} Henry\colon31-15=16miles \\ Tasha\colon35-25=10miles \end{gathered}$

Therefore, Henry's balloon travelled faster than Tasha's balloon