Problem 9 · 2013 Math Kangaroo
Easy
Ratios, Rates & Proportions
distance-speed-timeproportion
Tom and Laura stand directly opposite each other around a circular well. At the same moment they both begin to run clockwise around the well. Tom's speed is \(\frac{9}{8}\) of Laura's speed. How many full laps of the well will Laura run before Tom catches up with her for the first time?
Show answer
Answer: A — 4
Show hints
Hint 1 of 2
They start half a lap apart; Tom must close that gap running only a little faster.
Still stuck? Show hint 2 →
Hint 2 of 2
Work with the speed difference and how long it takes to make up half a lap.
Show solution
Approach: relative speed to close the gap
- Starting opposite means Tom is half a lap behind Laura.
- Tom gains on Laura at rate (9/8 − 1) = 1/8 of Laura's speed.
- To make up 1/2 lap at 1/8-lap-per-Laura-lap, Laura must run (1/2)÷(1/8) = 4 laps.
- So Laura completes 4 laps before being caught.
Mark:
· log in to save