Question

Mrs. McCarthy, the P.E. teacher, is pairing off students to race against each other. Kendrick can run 4 yards per second, and Lucia can run 9 yards per second. Mrs. McCarthy decides to give Kendrick a head start of 30 yards since he runs more slowly. Once the students start running, Lucia will quickly catch up to Kendrick. How long will that take? How far will Lucia have to run?

Answer 1

Lucia will catch up to Kendrick in 6 seconds after running 54 yards, considering she runs at a speed of 9 yards per second and Kendrick has a 30-yard head start.

Step-by-step explanation:

To determine how long it will take Lucia to catch up to Kendrick, we must first calculate when both students will have run the same distance. Given that Kendrick has a 30-yard head start and runs at a speed of 4 yards per second, and Lucia runs at a speed of 9 yards per second, we can set up an equation based on the time (t) it takes for Lucia to catch up:

Distance run by Kendrick = 4 yards/second * t + 30 yards

Distance run by Lucia = 9 yards/second * t

Setting these equal to each other gives us:

4t + 30 = 9t

To find the time (t), we need to solve for t:

30 = 9t - 4t

30 = 5t

t = 6 seconds

Therefore, it will take Lucia 6 seconds to catch up to Kendrick. To find out how far Lucia will have run, we simply multiply her speed by the time:

Distance Lucia runs = 9 yards/second * 6 seconds = 54 yards.

So, Lucia will have to run 54 yards to catch up with Kendrick.