Kate is going on a long distance car trip. She begins with 16 gallons of gas in her car and her car burns 3 gallons of gas each hour. If she ends her road trip with 1 gallon of gas left in the tank, how many hours was she driving

She was driving for 5 hours

Step-by-step explanation:

Let us solve the question

∵ Kate begins with 16 gallons of gas in her car

∵ Her car burns 3 gallons of gas each hour

→ That means the rate of burn of the gas is 3 gallons per hour

∵ She ends her road trip with 1 gallon of gas left in the tank

→ That means she used the difference between 16 and 1 gallons

∴ The number of gallons she used = 16 - 1 = 15 gallons

→ By using the ratio method

→ Gallon  :  hour

→  3          :  1

→  15        :  x

→ By using cross multiplication

∵ 3 × x = 15 × 1

∴ 3x = 15

→ Divide both sides by 3

∴ x = 5

∵ x represents the number of hours of her trip

∴ She was driving for 5 hours

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .