Sarin’s father crossing the Causeway part 2(Math Question)

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Read posting on Sarin’s father visits his friend in JB town to know about JB town as well as reading posting on Sarin’s father crossing the Causeway to know about the Johor-Singapore Causeway.

Read also posting on Sarin learns rate of change in school (Math Concept) to learn about concept of speed.

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?

Solution:   

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

Alternative solution:

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

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