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Upper primary school mathematics question UPQ41
Sarin’s father drives a car to JB town to meet his friend. He set off from Simei at a constant speed of 100km/h toward JB town. At the same time, a van and a lorry set off from JB town towards Simei at constant speeds of 60km/h and 50km/h respectively. If Sarin’s father drives pass the lorry exactly 12 min after passing the van, how far is Simei from JB Town?
When the car drives pass the lorry,
The distance travel by the lorry is 50/150 = 1/3 of the distance from JB town
From the car drives pass the van to drive pass the lorry needs 12mins,
Distance different between the lorry and the car is 160 × 12/60 = 32km
Ratio of speed of the car to the speed of the lorry = 100 : 50 = 2 : 1
Ratio of speed of the lorry to the speed of the van = 50 : 60 = 5 : 6
Ratio of distance travel by the lorry to the distance travel by the van = 5 : 6
Key note: Distance travel is proportional to the speed.
Distance travel is proportional to the time.
You can work out ratio model of distance as shown,
Per the above model,
1 unit = 32km
Total distance = 5 + 10 = 15units = 15 × 32 = 480km
The distance travel by the lorry was 50/150 = 1/3 of the distance from JB town
The distance travel by the van was 60/160 = 3/8 of the distance from JB town
Distance between the lorry and the van = 3/8 – 1/3 = 9/24 – 8/24 = 1/24
Total distance is 24units
Key note: The above model is taking reference to the car (Sarin’s father) based on the speed of 100km/h.
To travel 1 unit needs 12mins (Sarin’s father)
Total time to travel by the car from Simei to JB Town = 12 × 24 = 288mins = 4.8hrs
Total distance = 100 × 4.8 = 480km