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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 = 44x + 26 Car B: y = 36x + 66 After how many hours will the two cars be at the same distance from their starting point and what will that distance be?

 5 hours, 346 miles 5 hours, 246 miles 3 hours, 246 miles 3 hours, 346 miles

Respuesta :

mixter17

Hello!

The answer is:

5 hours, 246 miles.

Why?

Since we know the equations that represent the distances of both cars at certain times (function of time), we can calculate the time that they will be at the same distance by making their equation equal.

So, we are given the equations:

A-

[tex]y=44x+26[/tex]

B -

[tex]y=36x+66[/tex]

Now, by making both equation equal, we can calculate the time that they will have the same distance, so, we have:

[tex]44x+26=36x+66[/tex]

[tex]44x-36x=66-26[/tex]

[tex]8x=40[/tex]

[tex]x=\frac{40}{8}=5[/tex]

Hence, we have that they will have the same position after 5 hours.

Then, to calculate the distance, we need to substitute the obtained time in any of the given equations, so, substituting into A, we have:

[tex]y=44x+26[/tex]

[tex]y=44*5+26=220+26=246[/tex]

We have that the distance will be 246 miles.

Hence, we have that the answer is:

5 hours, 246 miles.

Have a nice day!

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