David and Gavin 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. David completed a full round in 50 s. Gavin completed a full round in 40 s.
- How long would it take for Gavin to overtake David for the first time?
- How far was Gavin ahead of David after 20 s?
(a)
LCM of 40 and 50 is 200.
Time taken for Gavin to overtake David
= 200 s
(b)
Gavin's speed
= 800 ÷ 40
= 20 m/s
David's speed
= 800 ÷ 50
= 16 m/s
Difference in speed
= 20 - 16
= 4 m/s
Distance David was behind Gavin after 20s
= 20 x 4
= 80 m
Answer(s): (a) 200s; (b) 80 m