Samuel and Samantha 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. Samuel completed a full round in 60 s. Samantha completed a full round in 50 s.
- How long would it take for Samantha to overtake Samuel for the first time?
- How far was Samantha ahead of Samuel after 18 s?
(a)
LCM of 50 and 60 is 300.
Time taken for Samantha to overtake Samuel
= 300 s
(b)
Samantha's speed
= 900 ÷ 50
= 18 m/s
Samuel's speed
= 900 ÷ 60
= 15 m/s
Difference in speed
= 18 - 15
= 3 m/s
Distance Samuel was behind Samantha after 18s
= 18 x 3
= 54 m
Answer(s): (a) 300s; (b) 54 m