Pond runners
Can you work out how much time it will be before Katherine laps James around the pond?
Age
14 to 16
Challenge level
Problem
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?
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Answer: $288$ seconds
Katherine $3$ minutes $1$ lap
$8$ minutes $2\frac23$ laps
James $8$ minutes $1\frac23$ laps (exactly $1$ lap behind)
$8$ minutes $\frac53$ laps
$\frac{8\times3}{5}$ minutes $1$ lap
$\frac{8\times3}{5}$ minutes $=\frac{8\times3}{5}\times60$ seconds $=288$ seconds