Question 991101
first car gets 15 miles per gallon.
second car gets 40 miles per gallon.
both cars went a total of 2000 miles for a total gas consumption of 75 gallons.


miles driven by first car is x.
miles driven by second car is y.


gallons consumed by first car is x / 15.
gallons consumed by second car is y / 40.


you have 2 equations.


x + y = 2000
x/15 + y/40 = 75


use the first equation to solve for y.


you get y = 2000 - x


replace y with 2000 - x in the second equation to get:


x/15 + (2000 - x) / 40 = 75


remove the fractions by multiplying both sides of the equation by 120.


you get:


120 * x / 15 + 120 * (2000 - x) / 40 = 75 * 120


simplify to get:


8 * x + 3 * (2000 - x) = 9000


simplify further by removing parentheses to get:


8 * x + 6000 - 3 * x = 9000


subtract 6000 from both sides of the equation to get:


8 * x - 3 * x = 3000


combine like terms to get:


5 * x = 3000


divide both sides of the equation by 5 to get:


x = 600


since y = 2000 - x, this means that:


y = 1400


the first car traveled 600 miles.
the second car traveled 1400 miles.


600 + 1400 = 2000
600 / 15 + 1400 / 40 = 40 + 35 = 75


numbers check out.


your solution is the the first car traveled 600 miles at 15 miles per gallon and the second car traveled 1400 miles at 40 miles per gallon.