Question

two cars are traveling down the highway with the same speed if the first car increases its speed by 1km/hr and the other car decreases its speed by 10km/hr,then the first car will cover the same distance in 2hrs as the second car in 3 hrs, what is the speed of the cars

Answer 1

Their speed is 32 km/h.

Explanation:

Since they're at the same speed, we can assign a variable to their speed called "x". When the first car increases its speed by 1 km/h, its new speed is "x + 1", while the other car decreases its speed by 10 km/h, so its new speed is "x - 10". The distance's formula can be expressed as below:

`\text{distance} = \text{speed}*\text{time}\\`

With the modifications to their speed, the distance the first car covers in 2 h and the distance the second car covers in 3 h is shown below:

`\text{distance}_(car1) = (x + 1)*2 \\\text{distance}_(car1) = 2*x + 2`

`\text{distance}_(car2) = \text{speed}*\text{time}\\\text{distance}_(car2) = (x - 10)*3\\\text{distance}_(car2) = 3*x - 30`

Since the distance covered by them must be the same, we can find the value of x that makes the expressions equal.

`2*x + 2 = 3*x - 30\\2*x - 3*x = -30 -2\\-x = -32\\x = 32`

Their speed is 32 km/h.