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? \( 55+10 h=60 h \quad 10+55 h=60 h \) How long will it take for Tristan to catch up to Lucy? Simplify any fractions.

To find the time \( h \) it will take for Tristan to catch up to Lucy, we can set up an equation based on the distances traveled by both of them. 1. **Distance traveled by Lucy**: Since Lucy is traveling at 55 miles per hour, the distance she travels in \( h \) hours is: \[ \text{Distance}_{\text{Lucy}} = 55h \] However, since she already has a 10-mile head start, the total distance from the starting point is: \[ \text{Distance}_{\text{Lucy}} = 55h + 10 \] 2. **Distance traveled by Tristan**: Tristan is traveling at 60 miles per hour, so the distance he travels in \( h \) hours is: \[ \text{Distance}_{\text{Tristan}} = 60h \] 3. **Setting the distances equal**: To find when Tristan catches up to Lucy, we set their distances equal: \[ 55h + 10 = 60h \] 4. **Solving for \( h \)**: \[ 10 = 60h - 55h \] \[ 10 = 5h \] \[ h = \frac{10}{5} = 2 \] So, it will take Tristan **2 hours** to catch up to Lucy. ### Summary: - The correct equation to use is \( 55h + 10 = 60h \). - It will take Tristan **2 hours** to catch up to Lucy.