Answer

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**Hint:**Assume the after time ‘t’ both the cars will be at the same position, i.e., they will meet. Consider \[{{d}_{A}}\] as the distance travelled by car A and \[{{d}_{B}}\] as the distance travelled by car B. Use the formula: - Speed \[\times \] time to find the values of \[{{d}_{A}}\] and \[{{d}_{B}}\] and equate the two distances to find the value of ‘t’. Use ‘t’ and (t – 1) as the time taken by car A and B respectively.

**Complete step by step solution:**

Here, we have been provided with the information regarding the journey of two cards with the speed of car B greater than that of car A. We have been asked to find the time at which car B will pass car A. So, basically we need to find the time at which they will meet at a particular point.

Now, let us assume that both the cars started from the point P and after a certain of time meet at point Q. So, we have,

Let us start counting the time from 9am and assume that after time ‘t’ both the cars meet. Since car A started the journey at 9am, it would have travelled ‘t’ hours. It is given that car B started the journey at 10am, so it would have travelled (t – 1) hours to meet at point Q.

Let, \[{{d}_{A}}\] = distance travelled by car A

Using the formula, speed \[\times \] time = distance, we have,

\[\Rightarrow {{d}_{A}}=40\times t\]

\[\Rightarrow {{d}_{A}}=40t\] ------ (1)

Also, \[{{d}_{B}}\] = distance travelled by car B

Using the formula, speed \[\times \] time = distance, we have,

\[\Rightarrow {{d}_{B}}=60\times \left( t-1 \right)\]

\[\Rightarrow {{d}_{B}}=60\left( t-1 \right)\] -------- (2)

Now, since both the cars have started from the same point and are meeting at the same point, so the distance travelled by them must be equal, so we have,

\[\Rightarrow {{d}_{A}}={{d}_{B}}\]

From equations (1) and (2), we get,

\[\Rightarrow 40t=60\left( t-1 \right)\]

Cancelling the common factors, we get,

\[\begin{align}

& \Rightarrow 2t=3\left( t-1 \right) \\

& \Rightarrow 2t=3t-3 \\

\end{align}\]

\[\Rightarrow t=3\] hours

Therefore, both the cars will meet after 3 hours, i.e. at 9 + 3 = 12pm.

**Hence, 12pm is our answer.**

**Note:**One may note that here we have taken the travelling time of car B as (t – 1) hours because it was given to us that car B started the journey 1 hours after car A started. So, to travel the same distance it required more speed. Remember that car B will pass car A just after the time they will meet so we have founded the time at which they will meet. You must remember the speed – time relation to solve the question.

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