Zoe and Caleb 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. Zoe completed a full round in 90 s. Caleb completed a full round in 60 s.
- How long would it take for Caleb to overtake Zoe for the first time?
- How far was Caleb ahead of Zoe after 15 s?
(a)
LCM of 60 and 90 is 180.
Time taken for Caleb to overtake Zoe
= 180 s
(b)
Caleb's speed
= 900 ÷ 60
= 15 m/s
Zoe's speed
= 900 ÷ 90
= 10 m/s
Difference in speed
= 15 - 10
= 5 m/s
Distance Zoe was behind Caleb after 15s
= 15 x 5
= 75 m
Answer(s): (a) 180s; (b) 75 m