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 = 45x + 20
Car B
y = 35x + 60
After how many hours will the two cars be at the same distance from their starting point and what will that distance be?
3 hours, 200 miles
3 hours, 180 miles
4 hours, 200 miles
4 hours, 180 miles

Answer 1

Given the equations for cars A and B, we are to find the time when their distances would be the same. Since y is the distance, we have to equate both expressions in terms of y to solve for the time (x):

y = 45x + 20
y = 35x + 60

45x + 20 = 35x + 60
45x - 35x = 60 - 20
10x = 40
x = 4 ; after 4 hours, they will be at the same distance from the starting point.

Using the obtained value of x, we solve for the distance using either of the equations:

y = 45(4) + 20
y = 180 + 20
y = 200

y = 35x + 60
y = 35(4) + 60
y = 140 + 60
y = 200

Therefore, the correct answer is 4 hours, 200 miles