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