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

Option A is correct

2 hours, 142 miles

Step-by-step 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] ;

⇒

Subtract 42x from both sides we have;

⇒

Subtract 32 from both sides we have;

Divide both sides by 13 we have;

x = 2 hours

Substitute in [1] we have;

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

5

step-by-step explanation:

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.