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 = 55x + 32

Car B
y = 42x + 58

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, 142 miles
2 hours, 145 miles
3 hours, 142 miles
3 hours, 145 miles

Answer 1

2hrs, 142miles
42x+58=55x+32
13x=26
x=2hrs <---- answer
42*2+58=142
55*2+32=142mi <----answer

Answer 2

Option A is correct

2 hours, 142 miles

Explanation:

As per the statement:

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 = 55x + 32 ....[1]

Car B

y = 42x + 58 ....[2]

We have to find after how many hours will the two cars be at the same distance from their starting point.

Since, two cars be at the same distance

equate [1] and [2] ;

⇒
`55x+32 = 42x+58`

Subtract 42x from both sides we have;

⇒
`13x+32 =58`

Subtract 32 from both sides we have;

`13x=26`

Divide both sides by 13 we have;

x = 2 hours

Substitute in [1] we have;

`y = 55(2)+32 = 110+32 = 142` miles

Therefore, after 2 hours will the two cars be at the same distance from their starting point and 142 miles will that distance be