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

Answer 1

To determine how long it will take for Tristan to catch up to Lucy, we can set up an equation based on their speeds and distances.

Let \( h \) represent the time in hours that Tristan drives after he leaves.

In that time, Lucy has already traveled for \( h + \frac{10}{55} \) hours (since she started 10 miles ahead and travelled at 55 mph), and she covers a distance of:

\[
\text{Distance traveled by Lucy} = 55(h + \frac{10}{55})
\]

In \( h \) hours, Tristan, who drives at 60 mph, covers:

\[
\text{Distance traveled by Tristan} = 60h
\]

Since Tristan needs to catch up to Lucy, the distances will be equal when he catches up:

\[
60h = 55(h + \frac{10}{55})
\]

Now, let's simplify and solve for \( h \):

1. Distribute the 55 on the right side:

\[
60h = 55h + 10
\]

2. Subtract \( 55h \) from both sides:

\[
60h - 55h = 10
\]

3. This simplifies to:

\[
5h = 10
\]

4. Divide both sides by 5:

\[
h = 2
\]

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