Lucy and Jack were planning to run on a circular track with a circumference of 900 m. Both of them started jogging together at the same start point and moved round the track in a clockwise direction at uniform speeds. Lucy completed a full round in 90 s. Jack completed a full round in 60 s.
- How long would it take for Jack to overtake Lucy for the first time?
- How far was Jack ahead of Lucy after 15 s?
(a)
LCM of 60 and 90 is 180.
Time taken for Jack to overtake Lucy
= 180 s
(b)
Jack's speed
= 900 ÷ 60
= 15 m/s
Lucy's speed
= 900 ÷ 90
= 10 m/s
Difference in speed
= 15 - 10
= 5 m/s
Distance Lucy was behind Jack after 15s
= 15 x 5
= 75 m
Answer(s): (a) 180s; (b) 75 m