SOLUTION: One car can travel 35 miles on a gallon of gasoline. The second can only travel 20 miles on a gallon of gasoline. Both cars want to take a trip. One car will follow the other, so e

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Question 920913: One car can travel 35 miles on a gallon of gasoline. The second can only travel 20 miles on a gallon of gasoline. Both cars want to take a trip. One car will follow the other, so each will travel the same distance. How far can the cars travel if they only have $308 to spend on gas, which costs $3.50 per gallon?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Fuel efficiency and cost.


Try forming a data table.

___________________rate____________volume__________distance
CARa_______________35_______________u______________d
Carb_______________20_______________v______________d
TOTAL_______________________________?

Car_a using u gallons, spending at $3.50 per gallon will spend u*(3.5) dollars.
Car_b using v gallons, spends v*(3.50) dollars.

THEY have $308, so highlight_green%283.5%28u%2Bv%29=308%29.

Look at the data table again. Both cars each go the same distance, d.
highlight_green%2835u=20v%29, according to basic rule for uniform rates, RX=Y for any rate being the ratio of Y to X.

The system of two linear equation in two unknown variables is
highlight%28system%283.5%28u%2Bv%29=308%2C35u=20v%29%29.
Solve this system for u and v, the gallons of fuel that each car must use; and then use u and v or either of them, to find the distance d that each car goes.