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