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.