Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and If they move in the opposite directions, they meet 1 hour and 20 minutes. Find the speeds of the cars.

By Ritesh|Updated : November 13th, 2022

The speed of car A is 35 km/hr and of car, B is 25 km/hr. Let the speed of the vehicle leaving from point A be x km/hr and the vehicle leaving from point B be y km/hr.

Given that the total distance = is 80 km

Also it is given that 1 hour 20 mins = 1 + 20/60 hours = 1 + ⅓ hours = 4/3 hour

According to the question we have, In 8 hours, a car travelling in the same direction will encounter another.

Therefore,

Distance travelled from B = 8y km

Because we know that Distance = Speed x Time

Distance travelled from A = 8x

Now, according to the given condition the equation formed is:

8x - 8y = 80 because the difference between the two automobiles' total distances = is 80km

The above equation becomes:

x - y = 10 ….(i)

The same is true for cars travelling in the opposite direction; they will collide in one hour and 20 minutes.

Distance travelled from B = 4y/3

Distance travelled from A = 4x/3

By adding them we get the total distance travelled or covered:

The total distance travelled = 4x/3 + 4y/3

According to the question, we can form the equation:

80 = 4x/3 + 4y/3

In simplification we get:

240 = 4x + 4y

60 = x + y …. (ii)

Equation (i) and Equation (ii) are added together to give us:

x + y + x - y = 60 + 10

x = 35

When we change the value of x in (ii), we obtain

60 = 35 + y

y = 60 - 35 = 25

Thus, the speed of the car as it leaves point A is 35 km/hr. An automobile leaves point B moving at a speed of 25 km/hr.

Summary:

Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and If they move in the opposite directions, they meet 1 hour and 20 minutes. Find the speeds of the cars.

Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and If they move in the opposite directions, they meet 1 hour and 20 minutes. The speed of car A is 35 km/hr and car B is 25 km/hr.

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