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. what does point f represent in this context?

Explanation:

Point F lies on line \(a\) (Josiah's distance equation \(y=10+2x\)). Substitute \(x=25\) (the x-value of point F) into the equation: \(y=10+2(25)=60\). This means after 25 seconds, Josiah is 60 meters from the starting line. It also shows that at this time, Chana (on line \(b: y=3x\), \(y=3(25)=75\)) has already passed Josiah, so point F specifically represents Josiah's position at 25 seconds, or more precisely, the time and distance where Josiah is at 60 meters after 25 seconds, while Chana is farther ahead.

Answer:

Point F represents that 25 seconds after they started skating, Josiah is 60 meters from the starting line (and at this time, Chana has already traveled 75 meters, so she is ahead of Josiah).