Jacob and Raeann 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. Jacob completed a full round in 60 s. Raeann completed a full round in 50 s.
- How long would it take for Raeann to overtake Jacob for the first time?
- How far was Raeann ahead of Jacob after 12 s?
(a)
LCM of 50 and 60 is 300.
Time taken for Raeann to overtake Jacob
= 300 s
(b)
Raeann's speed
= 600 ÷ 50
= 12 m/s
Jacob's speed
= 600 ÷ 60
= 10 m/s
Difference in speed
= 12 - 10
= 2 m/s
Distance Jacob was behind Raeann after 12s
= 12 x 2
= 24 m
Answer(s): (a) 300s; (b) 24 m