Let $2 d$ miles be the distance from the trailhead to the fire tower, where $d\textgreater0$. When Chantal meets Jean, the two have traveled for $$ \frac{d}{4}+\frac{d}{2}+\frac{d}{3}=d\left(\frac{1}{4}+\frac{1}{2}+\frac{1}{3}\right)=d\left(\frac{3}{12}+\frac{6}{12}+\frac{4}{12}\right)=\frac{13}{12} d $$ hours.  At that point, Jean has traveled for $d$ miles, so his average speed is $\frac{d}{\frac{13}{12} d}=(\mathbf{A}) \frac{12}{13}$ miles per hour. 
Chantal and Jean start hiking from a trailhead toward a fire tower. Jean is wearing a heavy backpack and walks slower. Chantal starts walking $4$ 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\textquotesingle s average speed, in miles per hour, until they meet? (2021 AMC 10A Problems, Question \#6) 
a. $\frac{12}{13}$ 
b. $$1$$ 
c. $\frac{13}{12}$ 
d. $\frac{24}{13}$ 
e. $$2$$ 