Question

The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below:

Car A
y = 60x + 10

Car B
y = 40x + 70

After how many hours will the two cars be at the same distance from their starting point and what will that distance be?

2 hours, 150 miles
2 hours, 190 miles
3 hours, 150 miles
3 hours, 190 miles

Answer 1

when the cars are at the same distance from the starting point the y will be the same for both of the equations.
which means that 60x + 10 = 40x + 70

⇒ 60x-40x=70-10
⇒ 20x=60
⇒ x=3 hours

now that we know the x we can choose an equation and solve it

60x3+10=y⇒
⇒y=180+10
⇒y=190 miles

the correct answer is the last one: 3 hours, 190 miles