Good Morning DeAsia,
Let x be the number of miles the first car traveled during the week.
That means the second car traveled 2200 -x
The gas mileage (fuel efficiency) is equal to miles traveled divided by gallons used.
The fuel efficiency of the first car is x/20 because the problem states that it consumed 20 gallons
The fuel efficiency of the second car is (2200 - x)/40
When I add these two together, I get 75
x/20 + (2200-x)/40 = 75
I'm going to multiply each term by 40 to clear the fractions
40x/20 + 40 (2200 - x)/40 = 40 * 75
2x + (2200 - x) = 3000
x + 2200 = 3000
x = 800
The fuel efficiency of the first car is miles per gallon. So 800 miles / 20 gallons = 40 miles per gallon
The second car traveled (2200 - 800) miles which equals 1400 miles
So the efficiency of the second car is 1400 miles / 40 gallons = 35 miles per gallon.
And to double check, they do add to 75