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

Answer 1

Answer: after driving 330 miles, the remaining fuel in each tank be the same.

Step-by-step explanation:

Let x represent the number of miles it will take for the the remaining fuel in each tank to be the same.

Jerry has a large car which holds 22 gallons of fuel and gets 20 miles per gallon. It means that the number of gallons needed to drive 1 mile is 1/20. Then the number of gallons needed to drive x miles is

1/20 × x = x/20

If the tank is full, then the number of gallons of fuel left after driving x miles is

22 - x/20

Kate has a smaller car which holds 16.5 gallons of fuel and gets 30 miles per gallon. It means that the number of gallons needed to drive 1 mile is 1/30. Then the number of gallons needed to drive x miles is

1/30 × x = x/30

If the tank is full, then the number of gallons of fuel left after driving x miles is

16.5 - x/30

For the remaining fuel in each tank to be the same, it means that

22 - x/20 = 16.5 - x/30

Multiplying both sides of the equation by 60(LCM), it becomes

1320 - 3x = 990 - 2x

- 2x + 3x = 1320 - 990

x = 330 miles