Victoria and Jacob were planning to run on a circular track with a circumference of 400 m. Both of them started jogging together at the same start point and moved round the track in a clockwise direction at uniform speeds. Victoria completed a full round in 80 s. Jacob completed a full round in 40 s.
- How long would it take for Jacob to overtake Victoria for the first time?
- How far was Jacob ahead of Victoria after 10 s?
(a)
LCM of 40 and 80 is 80.
Time taken for Jacob to overtake Victoria
= 80 s
(b)
Jacob's speed
= 400 ÷ 40
= 10 m/s
Victoria's speed
= 400 ÷ 80
= 5 m/s
Difference in speed
= 10 - 5
= 5 m/s
Distance Victoria was behind Jacob after 10s
= 10 x 5
= 50 m
Answer(s): (a) 80s; (b) 50 m