AMC 10 2021a Problem 6

Chantal and Jean start hiking from a trailhead toward a fire tower. Jean is wearing a heavy backpack and walks slower. Chantal starts walking at $4$ miles per hour. Halfway to the tower, the trail becomes really steep, and Chantal slows down to $2$ miles per hour. After reaching the tower, she immediately turns around and descends the steep part of the trail at $3$ miles per hour. She meets Jean at the halfway point. What was Jean's average speed, in miles per hour, until they meet? $\textbf{(A)} ~\frac{12}{13} \textbf{(B)} ~1 \textbf{(C)} ~\frac{13}{12} \textbf{(D)} ~\frac{24}{13} \textbf{(E)} ~2$