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