Question

Two cars leave at the same time from points A and B, the distance between them is 280 km. If the cars meet each other, they’ll meet in 2 hours. But if they go in the same direction, then the car going from point A will catch up with the car going from point B in 14 hours. What is the speed of both of the cars?

Answer 1

Set up the following equations:


`2x + 2y = 280`


`14x - 14y = 280`

x represents car A's speed, and y represents car B's speed.

We'll use elimination to solve this system of equations. Multiply the first equation by 7:


`(2x + 2y = 280) * 7 = 14x + 14y = 1960`


`14x - 14y = 280`

Combine both equations:


`28x = 2240`

Divide both sides by 28 to get x by itself:


`x = 80`

The speed of car A is 80 mph.

Since we now know the value of one of the variables, we can plug it into the first equation:


`2(80) + 2y = 280`


`160 + 2y = 280`

Subtract 160 from both sides.


`2y = 120`

Divide both sides by 2 to get y by itself:


`y = 60`

The speed of car B is 60 mph.