Your new hybrid car gets 40 mpg in the city and 32 mpg on the highway. The amount of gas you use, G (in gal), is given by G equals 1 over 40 c plus 1 over 32 h where c is the number of city miles driven and h is the number of highway miles driven. If you drove 150 miles in the city and used 8.5 gallons of gas, how many highway miles did you drive?

Question

Your new hybrid car gets 40 mpg in the city and 32 mpg on the highway.  The amount of gas you use, G (in gal), is given by G equals 1 over 40 c plus 1 over 32 h  where c is the number of city miles driven and h is the number of highway miles driven.  If you drove 150 miles in the city and used 8.5 gallons of gas, how many highway miles did you drive?

danjs · Answer

They give you the equation for total gas used. 
Total Gas = city rate* city miles + highway rate * highway miles
$$G=\frac{ 1 }{ 40 }*c + \frac{ 1 }{ 32 }*h$$

danjs · Answer

They then say in this instance, you drove 150 city miles, c=150, and used 8.5 gal gas, G=8.5

$$8.5=\frac{ 1 }{ 40 }*150 + \frac{ 1 }{ 32 }*h$$

you can solve for highway miles driven h