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Mathematics

Suppose a car starts from a place A and travels at a speed of 40 km/h towards another place B. At the same instance, another car starts from B and travels towards A at a speed of 30 km/h. If the distance between A and B is 100 km, after how much time will the cars meet?

Mathematical Modelling

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Answer

Step 1 : Formulation :

We will suppose that cars travel at a constant speed. So, any change of speed will be treated as irrelevant. If the cars meet after x hours, the first car would have traveled a distance of 40x km from A and second car would have traveled 30x km from B.

So the second car will be at a distance of (100 - 30x) km from A. So, the equation will be:

⇒ 40x = 100 - 30x

⇒ 40x + 30x = 100

⇒ 70x = 100 ….(1)

Step 2 : Finding the solution :

By solving equation (1), we get :

⇒ x = 10070=107\dfrac{100}{70} = \dfrac{10}{7} = 1.4 hours

Step 3 : Interpretation :

Since, x = 1.4 hours

Hence, the cars will meet after 1.4 hours.

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