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Hint: Assume two variables for the speeds of the two cars. Then, use the given information to form two equations involving the variables using the relation \[d = v \times t\]. Solve the two equations involving two unknowns by substitution and find the speeds of the car.

Complete step by step answer:

Let the speed of the car starting from A be x km/h and the speed of the car starting from B be y km/h.

It is given that the length of the highway between A and B is 100 km.

The distance d covered in time t, when traveling at the speed of v is given as follows:

\[d = v \times t..............(1)\]

If the two cars travel in the same direction, they meet in 5 hours. Let us take the speed of car A is greater than B. Then, the distance covered by car at A in 5 hours is the sum of the distance of the highway and the distance covered by car B. Hence, using equation (1), we have:

\[5x = 100 + 5y\]

Simplifying, by dividing both sides by 5, we have:

\[x = 20 + y..............(2)\]

If the two cars travel in the opposite direction, they meet in 1 hour. The total distance covered by both the cars together is equal to the length of the highway. Hence, using equation (1), we have:

\[x + y = 100.............(3)\]

Hence, we have two equations involving two unknowns.

Substituting equation (2) in equation (3), we get:

\[20 + y + y = 100\]

\[20 + 2y = 100\]

Solving for y, we have:

\[2y = 100 - 20\]

\[2y = 80\]

\[y = \dfrac{{80}}{2}\]

\[y = 40km/hr............(4)\]

Using equation (4) in equation (2), we get:

\[x = 20 + 40\]

\[x = 60km/hr\]

Hence, the speeds of the car are 60 km/hr and 40 km/hr.

Note: When writing the equation for the cars traveling in the same direction, consider the length of the highway also to be covered, otherwise, your answer will be wrong.

Complete step by step answer:

Let the speed of the car starting from A be x km/h and the speed of the car starting from B be y km/h.

It is given that the length of the highway between A and B is 100 km.

The distance d covered in time t, when traveling at the speed of v is given as follows:

\[d = v \times t..............(1)\]

If the two cars travel in the same direction, they meet in 5 hours. Let us take the speed of car A is greater than B. Then, the distance covered by car at A in 5 hours is the sum of the distance of the highway and the distance covered by car B. Hence, using equation (1), we have:

\[5x = 100 + 5y\]

Simplifying, by dividing both sides by 5, we have:

\[x = 20 + y..............(2)\]

If the two cars travel in the opposite direction, they meet in 1 hour. The total distance covered by both the cars together is equal to the length of the highway. Hence, using equation (1), we have:

\[x + y = 100.............(3)\]

Hence, we have two equations involving two unknowns.

Substituting equation (2) in equation (3), we get:

\[20 + y + y = 100\]

\[20 + 2y = 100\]

Solving for y, we have:

\[2y = 100 - 20\]

\[2y = 80\]

\[y = \dfrac{{80}}{2}\]

\[y = 40km/hr............(4)\]

Using equation (4) in equation (2), we get:

\[x = 20 + 40\]

\[x = 60km/hr\]

Hence, the speeds of the car are 60 km/hr and 40 km/hr.

Note: When writing the equation for the cars traveling in the same direction, consider the length of the highway also to be covered, otherwise, your answer will be wrong.

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