Question

chana and josiah started skating at the same time in the same direction, but josiah had a head start 10 meters past the starting line. chana skated 3 meters per second and josiah skated 2 meters per second. heres a graph that shows a system of equations for this scenario where x is the number of seconds since chana and josiah started skating and y is the distance in meters from the starting line.

Explanation:

Step1: Set up the equations

Chana's distance \(y = 3x\) (since she skates at 3 meters per second). Josiah's distance \(y = 10+2x\) (he has a 10 - meter head - start and skates at 2 meters per second).

Step2: Solve the system of equations

Set \(3x=10 + 2x\).
Subtract \(2x\) from both sides: \(3x-2x=10+2x - 2x\).
We get \(x = 10\).
Substitute \(x = 10\) into Chana's equation \(y = 3x\), then \(y=3\times10 = 30\).

Answer:

The point of intersection \(H\) is \((10,30)\), which means that after 10 seconds, both Chana and Josiah are 30 meters from the starting line.