Sophia and Alexander were planning to run on a circular track with a circumference of 700 m. Both of them started jogging together at the same start point and moved round the track in a clockwise direction at uniform speeds. Sophia completed a full round in 70 s. Alexander completed a full round in 50 s.
- How long would it take for Alexander to overtake Sophia for the first time?
- How far was Alexander ahead of Sophia after 14 s?
(a)
LCM of 50 and 70 is 350.
Time taken for Alexander to overtake Sophia
= 350 s
(b)
Alexander's speed
= 700 ÷ 50
= 14 m/s
Sophia's speed
= 700 ÷ 70
= 10 m/s
Difference in speed
= 14 - 10
= 4 m/s
Distance Sophia was behind Alexander after 14s
= 14 x 4
= 56 m
Answer(s): (a) 350s; (b) 56 m