Gem and Daniel started off from the same place and drove at uniform speeds in the same direction round a 45 km circular racing track. Gem completed each round in 60 minutes. Daniel took 100 minutes to complete each round.
- How far would Daniel be behind Gem after 1 hour?
- How long after they started would it take Gem to meet Daniel 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
Gem's speed
= 45 ÷ 1
= 45 x
11= 45 km/h
Daniel's speed
= 45 ÷ 1
23= 45 x
35= 27 km/h
Distance between Gem and Daniel after 1 hour
= 45 - 27
= 18 km
(b)
LCM of 60 and 100 = 300
300 min =
30060 h = 5 h
Time needed for Gem to meet Daniel for the first time = 5 h
Answer(s): (a) 18 km; (b) 5 h