Question 1090786
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Your car has a 12 gallon gas tank. you start off your week with a full tank. during the week you drive 145 miles. 
on Saturday you decide to take a road trip so you add 6 gallons of gas to your tank and leave town. 
you drive for 185 miles and your gas gauge reads exactly 1/4 full. what is your average gas mileage in miles per gallon?
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Instead of solving for the ratio  {{{miles/gallon}}}  I will solve the problem for the reciprocal ratio  {{{gallons/mile}}}.

Then I will convert my answer to miles per gallon.


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So, let x be the unknown ratio gallons-per-mile.

The full distance traveled is 145 + 185 miles = 330 miles.

The amount of the fuel spent is  {{{12 + 6 - (1/4)*12}}} = 12 + 6 - 3 = 15 gallons.

    Notice that {{{(1/4)*12}}} is the volume of the gas that left in the tank.


From the other side, the amount of the fuel spent is  330*x gallons


It gives you an equation

15 = 330x.


Hence,  x = {{{15/330}}} = {{{1/22}}}  {{{gallon/miles}}}.


Therefore, the answer to the problem's question is  22 miles per gallon.
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Solved.