Question

Helppop!!A car and van are driving on a highway. The table shows the amount y (in gallons) of gas in the cars 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=- 1/5x + 31. Which vehicle uses less gasoline per mile? How many miles must the vehicles travel for the amount of gas in each tank to be the same?

Answer 1

The car uses less gas

They use the same amount of gas after
`(640)/(7)` miles

Explanation:

Given

The table represents the car mileage

`y = -(1)/(5)x + 31` --- The van

First, calculate the car's slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

From the table, we have:

`(x_1,y_1) = (60,13.5);\ \ (x_2,y_2) = (180,10.5)`

So, we have:

`m = (10.5 - 13.5)/(180 - 60)`

`m = (-3)/(120)`

`m = -(1)/(40)`

Calculate the equation using:

`y = -(1)/(40)(x - 60)+13.5`

`y = -(1)/(40)x + 1.5+13.5`

`y = -(1)/(40)x + 15`

`m = -(1)/(40)` implies that for every mile traveled, the car uses 1/40 gallon of gas

Also:

`y = -(1)/(5)x + 31` --- The van

By comparison to:
`y = mx + b`

`m = -(1)/(5)`

This implies that for every mile traveled, the van uses 1/5 gallon of gas.

By comparison:

`1/40 < 1/5`

This means that the car uses less gas

Solving (b): Distance traveled for them to use the same amount of gas.

We have:

`y = -(1)/(5)x + 31` --- The van

`y = -(1)/(40)x + 15` --- The car

Equate both

`-(1)/(5)x + 31 =-(1)/(40)x + 15`

Collect like terms

`(1)/(40)x -(1)/(5)x =-31 + 15`

`(1)/(40)x -(1)/(5)x =-16`

Take LCM

`(x - 8x)/(40) = -16`

`(- 7x)/(40) = -16`

Solve for -7x

`-7x = -640`

Solve for x

`x = (640)/(7)`