Question

write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
mrs. lam, the p.e. teacher, is pairing off students to race against each other. shane can run 6 yards per second, and kamal can run 9 yards per second. mrs. lam decides to give shane a head start of 48 yards since he runs more slowly. once the students start running, kamal will quickly catch up to shane. how far will kamal have to run? how long will that take?
kamal will catch up to shane after running

yards in

seconds.

Explanation:

Step1: Define variables

Let \( t \) be the time (in seconds) Kamal runs until he catches up with Shane, and let \( d \) be the distance (in yards) Kamal runs.

Step2: Write equations for distance

• Shane has a 48 - yard head start and runs at 6 yards per second. So the distance Shane runs in \( t \) seconds is \( 48 + 6t \).
• Kamal runs at 9 yards per second, so the distance Kamal runs in \( t \) seconds is \( d = 9t \).

When Kamal catches up with Shane, their distances are equal. So we set up the equation:
\( 9t=48 + 6t \)

Step3: Solve for \( t \)

Subtract \( 6t \) from both sides of the equation:
\( 9t-6t=48 + 6t-6t \)
\( 3t = 48 \)
Divide both sides by 3:
\( t=\frac{48}{3}=16 \) seconds.

Step4: Find the distance Kamal runs

Substitute \( t = 16 \) into the equation for Kamal's distance \( d = 9t \):
\( d=9\times16 = 144 \) yards.

Answer:

Kamal will catch up to Shane after running 144 yards in 16 seconds.