two cars are traveling down the highway with the same speed. if the first car increases its speed by 1 km per hour and the other car decreases its speed by 10 km per hour then the first car will cover the same distance in 2 hours as a second car in 3 hours what is the speed of the cars

Original speed = 32 km/h

First car's new speed = 33 km/h

Second car's new speed = 22 km/h

Step-by-step explanation:

"two cars are traveling down the highway with the same speed"

Let the original speed of both cars be x.

"the first car increases its speed by 1 km per hour"

Now its speed is x + 1.

"the other car decreases its speed by 10 km per hour"

Now its speed is x - 10.

Now we need a relationship between speed, distance, and speed.

speed = distance/time

Multiply both sides by time and switch sides.

distance = speed * time

In 2 hours, the first car covers (speed * time for first car):

distance = 2 * (x + 1)

In 3 hours, the second car covers (speed * time for second car)

distance = 3 * (x - 10)

The distances are equal, so we set them equal and solve the equation for x.

2 (x + 1) = 3 (x - 10)

2x + 2 = 3x - 30

2 = x - 30

32 = x

x = 32

The original speed of the cars was 32 km/h

After the speeds changed, the first car's speed is

x + 1 = 32 + 1 = 33 km/h

The second car's speed becomes

x - 10 = 32 - 10 = 22 km/h

Let's check:

In 2 hours, the first car covers 2 h * 33 km/h = 66 km

In 3 hours, the second car covers 3 h * 22 km/h = 66 km

The distances are the same, so our answer is correct.