Tommy and Sophia 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. Tommy completed a full round in 50 s. Sophia completed a full round in 40 s.
- How long would it take for Sophia to overtake Tommy for the first time?
- How far was Sophia ahead of Tommy after 10 s?
(a)
LCM of 40 and 50 is 200.
Time taken for Sophia to overtake Tommy
= 200 s
(b)
Sophia's speed
= 400 ÷ 40
= 10 m/s
Tommy's speed
= 400 ÷ 50
= 8 m/s
Difference in speed
= 10 - 8
= 2 m/s
Distance Tommy was behind Sophia after 10s
= 10 x 2
= 20 m
Answer(s): (a) 200s; (b) 20 m