Final answer:
In this scenario, Chana and Josiah start skating at the same time in the same direction, but Josiah has a head start of 10 meters. Chana skates at a speed of 3 meters per second and Josiah skates at a speed of 2 meters per second. Josiah catches up with Chana after 10 seconds, and at that time, both of them are 30 meters from the starting line.
Step-by-step explanation:
In this scenario, Chana and Josiah are skating in the same direction, but Josiah has a head start of 10 meters. Chana is skating at a speed of 3 meters per second, while Josiah is skating at a speed of 2 meters per second.
To determine when Josiah catches up with Chana, we need to find the time it takes for them to cover the same distance. Let's call this time 't'.
Chana's position, y1, can be represented as y1 = 3t, since she is skating at a constant speed of 3 meters per second.
Josiah's position, y2, can be represented as y2 = 2t + 10, since he has a head start of 10 meters and is skating at a constant speed of 2 meters per second.
To find the time when they are at the same position, we can set y1 equal to y2 and solve for t: 3t = 2t + 10. Simplifying the equation, we get t = 10.
Thus, Josiah catches up with Chana after 10 seconds. To find their positions, we substitute t = 10 into either of the original equations. Let's use Chana's equation: y = 3t = 3 x 10 = 30 meters.
Therefore, after Josiah catches up with Chana, they will both be 30 meters from the starting line.