1. distance and rate problem

how long will it take someone running at 12 mph to catch up to someone walking at 5 mph with an hour and half head start?

I keep getting 15/24 but the answer sheet says it is 15/14? is the answer on the answer sheet a typo or am i doing it wrong?

2. I'm assuming here that t = time for the jogger:
walker: $d = 5(t + 1.5)$
jogger: $d = 12t$

Set the equations equal:
\begin{aligned}
5(t + 1.5) &= 12t \\
5t + 7.5 &= 12t \\
7t &= 7.5 \\
t &= \frac{7.5}{7} \\
t &= \frac{15}{14}
\end{aligned}

15/14 hours ≈ 1 hr, 4 min, 17.14 sec

3. look at this !

look at this sketch!

4. ooohh! i get it! thanks a lot!