Question

Jerry has a large car which holds 222222 gallons of fuel and gets 202020 miles per gallon. kate has a smaller car which holds 16.516.516, point, 5 gallons of fuel and gets 303030 miles per gallon. if both cars have a full tank of fuel now and drive the same distance, in how many miles will the remaining fuel in each tank be the same? choose 1 answer: 320320

Answer 1

The remaining fuel in each tank will be the same after driving 665,000 miles.

Step-by-step explanation:

To find the number of miles at which the remaining fuel in each tank will be the same, we need to set up an equation. Let's assume that after driving x miles, the remaining fuel in Jerry's car is the same as the remaining fuel in Kate's car.

Jerry's car:

Remaining fuel = 222222 - (x / 202020) gallons

Kate's car:

Remaining fuel = 16.5 - (x / 303030) gallons

Setting these two expressions equal to each other:

222222 - (x / 202020) = 16.5 - (x / 303030)

Multiplying both sides of the equation by 202020 * 303030 to eliminate the denominators:

222222 * 303030 - (x * 303030) = 16.5 * 202020 - (x * 202020)

Simplifying the equation:

67474866660 - 303030x = 3333333 - 202020x

Combining like terms:

101010x = 67141533327

Dividing both sides of the equation by 101010:

x = 67141533327 / 101010

x = 665000

Therefore, the remaining fuel in each tank will be the same after driving 665,000 miles.

Answer 2

We are going to define the following linear functions:
g1 = - (1/20) * d + 22
g2 = - (1/30) * d + 16.5
where:
g1: amount of fuel remaining in car 1
g2: amount of fuel remaining in car 2
d: distance traveled
So we have g1 = g2
- (1/20) * d + 22 = - (1/30) * d + 16.5
We cleared d:
d (- (1/20) + (1/30)) = 16.5 - 22
d = (16.5 - 22) / (- (1/20) + (1/30))
d = 330 miles
Answer:
The remaining fuel in each tank will be the same in:
d = 330 miles