Hannah and Gabriel were planning to run on a circular track with a circumference of 1000 m. Both of them started jogging together at the same start point and moved round the track in a clockwise direction at uniform speeds. Hannah completed a full round in 50 s. Gabriel completed a full round in 40 s.
- How long would it take for Gabriel to overtake Hannah for the first time?
- How far was Gabriel ahead of Hannah after 25 s?
(a)
LCM of 40 and 50 is 200.
Time taken for Gabriel to overtake Hannah
= 200 s
(b)
Gabriel's speed
= 1000 ÷ 40
= 25 m/s
Hannah's speed
= 1000 ÷ 50
= 20 m/s
Difference in speed
= 25 - 20
= 5 m/s
Distance Hannah was behind Gabriel after 25s
= 25 x 5
= 125 m
Answer(s): (a) 200s; (b) 125 m