Sophia and Tommy 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. Sophia completed a full round in 80 s. Tommy completed a full round in 50 s.
- How long would it take for Tommy to overtake Sophia for the first time?
- How far was Tommy ahead of Sophia after 8 s?
(a)
LCM of 50 and 80 is 400.
Time taken for Tommy to overtake Sophia
= 400 s
(b)
Tommy's speed
= 400 ÷ 50
= 8 m/s
Sophia's speed
= 400 ÷ 80
= 5 m/s
Difference in speed
= 8 - 5
= 3 m/s
Distance Sophia was behind Tommy after 8s
= 8 x 3
= 24 m
Answer(s): (a) 400s; (b) 24 m