A car and a van are driving on a highway. The table shows the amount y (in gallons) of gas in the car's gas tank after driving x miles. The amount of gas in the van's gas tank after driving x miles is represented by the equation y=−112x+40. Which vehicle uses less gasoline per mile? How many miles must the vehicles travel for the amount of gas in each gas tank to be the same?

Car
Miles traveled, x Gallons of gas in tank, y
60 15
120 13
180 11
240 9

The amount of gas in each tank is the same after _ miles.

Given the table that shows the amount y (in gallons) of gas in the car's gas tank after driving x miles. We need to get the required equation of the table

The standard equation is expressed as y = mx + b

m is rate

b is the intercept

Get the required rate:

[tex]m=\frac{120-60}{13-15}\\m=\frac{60}{-2}\\m=-30\\[/tex]

Get the intercept:

Using (9, 240) and m = -30

240 = -30(9) + b

240 = -270 + b

b = 510

The required equation will be y = -30x + 510

If the amount of gas in each gas tank to be the same, then;

-30x + 510 = -112x + 40

-30x + 112x = 40 - 510

82x = -470

x = 470/-82

x = 5.73miles

This shows that the amount of gas in each tank is the same after 5.73 miles.

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