Jonathan and Matthew 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. Jonathan completed a full round in 80 s. Matthew completed a full round in 40 s.
- How long would it take for Matthew to overtake Jonathan for the first time?
- How far was Matthew ahead of Jonathan after 20 s?
(a)
LCM of 40 and 80 is 80.
Time taken for Matthew to overtake Jonathan
= 80 s
(b)
Matthew's speed
= 800 ÷ 40
= 20 m/s
Jonathan's speed
= 800 ÷ 80
= 10 m/s
Difference in speed
= 20 - 10
= 10 m/s
Distance Jonathan was behind Matthew after 20s
= 20 x 10
= 200 m
Answer(s): (a) 80s; (b) 200 m