Question

or
Last Saturday, Erin and Krysta each biked the Prairie Point Trail, a 20-mile path leading to the peak of Prairie Point Mountain. Both girls started at 7:00 A.M., heading toward the peak. Erin started at the trailhead and biked at a constant speed of 10 miles per hour. Krysta started at an entry point 3 miles ahead of the trailhead and rode at a steady pace of 8 miles per hour.
If each girl kept a constant speed, which equation can you use to find h, the number of hours it took for Erin to catch up to Krysta?
How long did it take for Erin to catch up to Krysta?
Simplify any fractions.
hours

Answer 1

To solve the problem, we can set up an equation based on the distances traveled by both Erin and Krysta.

Let's denote:
- \( h \) = time in hours that Erin takes to catch up to Krysta.
- Distance that Erin travels = speed of Erin × time = \( 10h \).
- Distance that Krysta travels = speed of Krysta × time = \( 8h \).

Since Krysta started 3 miles ahead of Erin, her distance traveled can be expressed as:

\[
\text{Distance traveled by Krysta} = 8h + 3
\]

To find out when Erin catches up with Krysta, we set the distances equal to each other:

\[
10h = 8h + 3
\]

Now, we can solve for \( h \):

1. Subtract \( 8h \) from both sides:
\[
10h - 8h = 3
\]

2. This simplifies to:
\[
2h = 3
\]

3. Divide by 2:
\[
h = \frac{3}{2} \text{ hours}
\]

Converting \( \frac{3}{2} \) to hours and minutes:
- \( \frac{3}{2} \) hours = 1 hour and 30 minutes.

Thus, it took Erin \( \frac{3}{2} \) hours (or 1 hour and 30 minutes) to catch up to Krysta.