Hazel and Matthew were planning to run on a circular track with a circumference of 900 m. Both of them started jogging together at the same start point and moved round the track in a clockwise direction at uniform speeds. Hazel completed a full round in 90 s. Matthew completed a full round in 50 s.
- How long would it take for Matthew to overtake Hazel for the first time?
- How far was Matthew ahead of Hazel after 18 s?
(a)
LCM of 50 and 90 is 450.
Time taken for Matthew to overtake Hazel
= 450 s
(b)
Matthew's speed
= 900 ÷ 50
= 18 m/s
Hazel's speed
= 900 ÷ 90
= 10 m/s
Difference in speed
= 18 - 10
= 8 m/s
Distance Hazel was behind Matthew after 18s
= 18 x 8
= 144 m
Answer(s): (a) 450s; (b) 144 m