Mathematical Modelling — Question 2

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 = $\dfrac{100}{70} = \dfrac{10}{7}$ = 1.4 hours

Step 3 : Interpretation :

Since, x = 1.4 hours

Hence, the cars will meet after 1.4 hours.