Final answer:
Julie and Sarah will catch up to each other after running 7.5 meters.
Step-by-step explanation:
Julie and Sarah are racing each other. Julie runs 5 meters per hour and gets a 3-meter head start. Sarah runs 3 meters per hour and gets a 5-meter head start. To find out how many meters they have to run before they catch up to each other, we need to determine when their distances are equal.
Let's assume that they catch up to each other after t hours. During this time, Julie would have covered a distance of 5t meters, and Sarah would have covered a distance of 3t meters. Since Julie starts with a 3-meter head start, their distances will be equal when:
5t = 3t + 3
Solving for t:
2t = 3
t = 3/2
Substituting the value of t back into the equations, we can find the distance they have to run:
Distance = 5t
= 5(3/2)
= 7.5 meters
Therefore, they have to run 7.5 meters before they will catch up to each other.