Rachel and Gabriel started off from the same place and drove at uniform speeds in the same direction round a 30 km circular racing track. Rachel completed each round in 60 minutes. Gabriel took 100 minutes to complete each round.
- How far would Gabriel be behind Rachel after 1 hour?
- How long after they started would it take Rachel to meet Gabriel for the first time? Express your answer as a whole or mixed number in h.
(a)
60 min = 1 h
1 min =
160 h
60 min =
6060 h = 1 h
100 min =
10060 h = 1
23 h
Rachel's speed
= 30 ÷ 1
= 30 x
11= 30 km/h
Gabriel's speed
= 30 ÷ 1
23= 30 x
35= 18 km/h
Distance between Rachel and Gabriel after 1 hour
= 30 - 18
= 12 km
(b)
LCM of 60 and 100 = 300
300 min =
30060 h = 5 h
Time needed for Rachel to meet Gabriel for the first time = 5 h
Answer(s): (a) 12 km; (b) 5 h