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 = 52x + 70

Car B:
y = 54x + 56

After how many hours will the two cars be at the same distance from their starting point and what will that distance be? (1 point)

a
6 hours, 420 miles

b
6 hours, 434 miles

c
7 hours, 420 miles

d
7 hours, 434 miles

Answer 1

d) 7 hours, 434 miles

Explanation:

We need to find the time when the distances of both cars from their starting points will be equal. That is, we need to find the value of x for which the equations for Car A and Car B will give the same value of y. We can set the two equations equal to each other and solve for x:

52x + 70 = 54x + 56

Subtracting 52x and 56 from both sides, we get:

14 = 2x

x = 7

So the two cars will be at the same distance from their starting points after 7 hours. To find the distance at that time, we can substitute x=7 into either of the two equations and solve for y:

y = 52(7) + 70 = 434 (using the equation for Car A)

y = 54(7) + 56 = 386 (using the equation for Car B)

Therefore, the correct answer is:

d) 7 hours, 434 miles