Question - Running Around a Circular Well

Let the number of complete laps Laura completes before Tom catches up be \( L \).

Since Tom completes 10 laps while Laura completes 8 laps, the ratio of their speeds is \( \frac{10}{8} = \frac{5}{4} \).

If we set the time taken for Laura to complete \( L \) laps as \( t \), then Tom completes \( \frac{5}{4}L \) laps in the same time, meaning:

1 lap for Tom when Laura completes \( \frac{4}{5} \) laps.

Thus, when they run together, for every 10 laps of Tom, Laura runs 8 laps. Therefore, to find the total laps before Tom catches her:

Set the equation \( 10x = 8(x + 1) \):

\( 10x = 8x + 8 \)

\( 2x = 8 \)

\( x = 4 \)

Hence, Laura completes 4 laps before Tom catches her. The answer is:

4 complete laps.