Caleb and Alexander were planning to run on a circular track with a circumference of 800 m. Both of them started jogging together at the same start point and moved round the track in a clockwise direction at uniform speeds. Caleb completed a full round in 80 s. Alexander completed a full round in 40 s.
- How long would it take for Alexander to overtake Caleb for the first time?
- How far was Alexander ahead of Caleb after 20 s?
(a)
LCM of 40 and 80 is 80.
Time taken for Alexander to overtake Caleb
= 80 s
(b)
Alexander's speed
= 800 ÷ 40
= 20 m/s
Caleb's speed
= 800 ÷ 80
= 10 m/s
Difference in speed
= 20 - 10
= 10 m/s
Distance Caleb was behind Alexander after 20s
= 20 x 10
= 200 m
Answer(s): (a) 80s; (b) 200 m