10. Katherine and James are jogging in the same direction around a pond. They start at the same time and from the same place and each jogs at a constant speed. Katherine, the faster jogger, takes 3 minutes to complete one lap and first overtakes James 8 minutes after starting. How many seconds does it take James to complete one lap?
10. 288 Katherine catches James after 8 minutes when she has jogged $\frac{8}{3}$ laps. In that time, James will have jogged one lap fewer so will have jogged $\frac{5}{3}$ laps. Therefore, James jogs $\frac{5}{3}$ laps in 8 minutes which is the same as 480 seconds. Hence he will jog $\frac{1}{3}$ of a lap in 96 seconds and so he jogs a whole lap in 288 seconds.