Question

two cars are traveling down the highway with the same speed. If the first car increases its speed by 10 kilometers per hour, and the other car decreases its speed by 10 kilometers per hour, then the first car will cover the same distance for 2 hours as the second car for 3 hours. what is the speed of the cars?

Answer 1

The initial speed of the cars was 50 km/h, calculated using algebra by setting two equations equal to each other representing the distances covered by both cars, considering their respective speed changes.

Step-by-step explanation:

We are given that two cars are traveling at the same speed initially. When the first car increases its speed by 10 km/h and the second car decreases its speed by 10 km/h, the first car covers the same distance in 2 hours while the second car takes 3 hours to cover the same distance. We can use algebra to find the initial speed of the cars.

Step-by-step explanation:

Let the initial speed of both cars be v km/h.

The first car's increased speed is (v + 10) km/h.

The second car's decreased speed is (v - 10) km/h.

Since distance = speed × time, we set up two equations representing the distances covered by both cars. For the first car: Distance = (v + 10) × 2, for the second car: Distance = (v - 10) × 3.

Since both distances are equal, we have (v + 10) × 2 = (v - 10) × 3.

Solve this equation: 2v + 20 = 3v - 30.

Rearrange and solve for v: v = 50 km/h.

This calculation shows that the initial speed of the cars was 50 km/h before one increased its speed and the other decreased it.