David and Elizabeth were planning to run on a circular track with a circumference of 600 m. Both of them started jogging together at the same start point and moved round the track in a clockwise direction at uniform speeds. David completed a full round in 60 s. Elizabeth completed a full round in 40 s.
- How long would it take for Elizabeth to overtake David for the first time?
- How far was Elizabeth ahead of David after 15 s?
(a)
LCM of 40 and 60 is 120.
Time taken for Elizabeth to overtake David
= 120 s
(b)
Elizabeth's speed
= 600 ÷ 40
= 15 m/s
David's speed
= 600 ÷ 60
= 10 m/s
Difference in speed
= 15 - 10
= 5 m/s
Distance David was behind Elizabeth after 15s
= 15 x 5
= 75 m
Answer(s): (a) 120s; (b) 75 m