Problem 21 · 2009 Math Kangaroo
Stretch
Ratios, Rates & Proportions
distance-speed-timeoff-by-one
Two runners each run at constant speed around a racetrack. Both start at the same time at the same point. A is faster than B, takes 3 minutes to cover one lap, and overtakes B for the first time after 8 minutes. How long does B take to cover one lap?
Show answer
Answer: D — 4 min 48 sec
Show hints
Hint 1 of 2
‘First overtake’ means A has run exactly one extra full lap compared with B.
Still stuck? Show hint 2 →
Hint 2 of 2
Set A’s laps minus B’s laps equal to 1 at the 8-minute mark and solve for B’s lap time.
Show solution
Approach: first overtaking = exactly one lap ahead
- In 8 minutes A completes 8/3 laps; B completes 8/T laps for lap time T.
- First overtaking means 8/3 − 8/T = 1, so 8/T = 5/3 and T = 24/5 minutes.
- That is 4 min 48 sec.
Mark:
· log in to save