Thread: please help--- word problem

small car and a van share 110 gallons of gas. car gets twice as many miles to the gallon. if the car drove 600 miles and the van drove 800 miles. How many gallons of gas did the van use?

I believe I know the answer but I'm not sure how to set the problem up in algebraic format.

what about setting it up like this and then solve for Vgal

1) Cgal + Vgal = 110 gal
2) (2*600mi)/(Cgal) + (800mi)/(Vgal) = (1400/110)(mi/gal)

as read the Car gets twice as many miles 2*600mi/Cgal to the gallon

Let m be the mileage of the van
Then 2m is the mileage of the car.
Let g be the gallons the van had
Then 110-g is the gallons the car had.
Thus, since the car traveled 600 miles and the van 800 miles we have,
(110-g)2m=600
gm=800
This is a system of 2 equations, just divide both equations.
Thus, the truck had 80 gallons and took 10 miles to the gallons, and the car had 30 gallons and took 20 miles to the gallon.