Question

The Coleman family is moving to a new home on the other side of the state. Lucy Coleman leaves first, hauling a trailer and traveling at a constant speed of 55 miles per hour. When her husband, Tristan, leaves in his car, Lucy is already 10 miles away. Tristan drives at a constant speed of 60 miles per hour.
Which equation can you use to find h, the number of hours it will take for Tristan to catch up to Lucy?
How long will it take for Tristan to catch up to Lucy?
Simplify any fractions.
hours
10+55h=60h 55+10h=60h

Answer 1

To find the time it takes for Tristan to catch up to Lucy, we can start by setting up an equation based on their distances traveled.

Lucy leaves first and travels at a speed of 55 miles per hour. If he travels for \( h \) hours, the distance she covers is:
\[
\text{Distance}_{\text{Lucy}} = 55h + 10
\]
This accounts for the fact that she has a 10-mile head start.

Tristan, on the other hand, travels at a speed of 60 miles per hour. The distance he covers in \( h \) hours is:
\[
\text{Distance}_{\text{Tristan}} = 60h
\]

To find the time when Tristan catches up to Lucy, we set the distances equal to each other:
\[
55h + 10 = 60h
\]

Now, we can solve for \( h \):
1. Subtract \( 55h \) from both sides:
\[
10 = 60h - 55h
\]
\[
10 = 5h
\]
2. Divide both sides by 5:
\[
h = 2
\]

Thus, it will take Tristan **2 hours** to catch up to Lucy.

For the second part of your question, you provided two equations: \( 10 + 55h = 60h \) and \( 55 + 10h = 60h \). The first equation \( 10 + 55h = 60h \) is the correct setup based on the context of the problem.

The solution is:
\[
h = 2 \text{ hours}
\]