Question

pearly and peggy sue left their dorm room at the same time and headed in opposite directions. After 9 hours they were 1,080 miles apart. if pearly drove 20mph faster than peggy sue, how fast did peggy sue drive?

Answer 1

Let \( r \) be the speed of Peggy Sue in miles per hour. Then Pearly's speed is \( r + 20 \) mph. Since they are traveling in opposite directions, we can express the total distance they are apart after 9 hours as:

\[
\text{Distance} = \text{Speed of Peggy Sue} \times \text{Time} + \text{Speed of Pearly} \times \text{Time}
\]

After 9 hours, their total distance apart is 1,080 miles, so we can set up the equation:

\[
9r + 9(r + 20) = 1080
\]

Now, simplify the equation:

\[
9r + 9r + 180 = 1080
\]
\[
18r + 180 = 1080
\]

Next, subtract 180 from both sides:

\[
18r = 900
\]

Now, divide both sides by 18:

\[
r = 50
\]

So, Peggy Sue drove at a speed of **50 miles per hour**.

To find Pearly's speed, we add 20 mph:

\[
r + 20 = 50 + 20 = 70
\]

Pearly drove at a speed of **70 miles per hour**.

In summary, Peggy Sue drove at **50 mph**.