Michael and Luke were planning to run on a circular track with a circumference of 400 m. Both of them started jogging together at the same start point and moved round the track in a clockwise direction at uniform speeds. Michael completed a full round in 80 s. Luke completed a full round in 50 s.
- How long would it take for Luke to overtake Michael for the first time?
- How far was Luke ahead of Michael after 8 s?
(a)
LCM of 50 and 80 is 400.
Time taken for Luke to overtake Michael
= 400 s
(b)
Luke's speed
= 400 ÷ 50
= 8 m/s
Michael's speed
= 400 ÷ 80
= 5 m/s
Difference in speed
= 8 - 5
= 3 m/s
Distance Michael was behind Luke after 8s
= 8 x 3
= 24 m
Answer(s): (a) 400s; (b) 24 m