Rachel and Gem started off at the same spot and ran at average speeds round a 6-km circular path. Rachel took 12 minutes to complete each round. Gem completed each round in 25 minutes.
- How far ahead of Gem would Rachel be after 10 minute? Express your answer in metres.
- How long would it take Rachel to meet Gem for the first time?
- How many rounds would Rachel have completed by then?
(a)
Rachel's speed =
612 =
12 km/min
Gem's speed =
625 km/min
Difference in speeds
=
12 -
625=
2550 -
1250=
1350 km/min
Distance between Rachel and Gem after 10 min
= 10 x
1350= 2
3050 km
1 km = 1000 m
2
3050 km = 2
3050 x 1000 = 2600
(b)
LCM of 12 and 25 = 300
60 min = 1 h
300 min = 300 ÷ 60 = 5
Rachel and Gem will meet for the first time after 5 h.
(c)
Rounds Rachel completed
= 300 ÷ 12
= 25
Answer(s): (a) 2600 m; (b) 5 h; (c) 25