Xuan and Jack started off from the same place and drove at uniform speeds in the same direction round a 60 km circular racing track. Xuan completed each round in 50 minutes. Jack took 80 minutes to complete each round.
- How far would Jack be behind Xuan after 1 hour?
- How long after they started would it take Xuan to meet Jack for the first time? Express your answer as a whole or mixed number in h.
(a)
60 min = 1 h
1 min =
160 h
50 min =
5060 h =
56 h
80 min =
8060 h = 1
13 h
Xuan's speed
= 60 ÷
56= 60 x
65= 72 km/h
Jack's speed
= 60 ÷ 1
13= 60 x
34= 45 km/h
Distance between Xuan and Jack after 1 hour
= 72 - 45
= 27 km
(b)
LCM of 50 and 80 = 400
400 min =
40060 h = 6
23 h
Time needed for Xuan to meet Jack for the first time = 6
23 h
Answer(s): (a) 27 km; (b) 6
23 h