Sophia and Julie 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. Sophia completed a full round in 50 s. Julie completed a full round in 40 s.
- How long would it take for Julie to overtake Sophia for the first time?
- How far was Julie ahead of Sophia after 15 s?
(a)
LCM of 40 and 50 is 200.
Time taken for Julie to overtake Sophia
= 200 s
(b)
Julie's speed
= 600 ÷ 40
= 15 m/s
Sophia's speed
= 600 ÷ 50
= 12 m/s
Difference in speed
= 15 - 12
= 3 m/s
Distance Sophia was behind Julie after 15s
= 15 x 3
= 45 m
Answer(s): (a) 200s; (b) 45 m