Expert: Josh - 2/17/2004

Question
Donna's new car gets 22 miles per gallon (mpg) in the city and 34 mpg on the highway.  Write a compound inequality which represents the number of miles she can drive on 14 gallons of gas.

308<14X<476  ?

Answer
Hi Joanna,

Let the gas consumption rate in the city be Rc,
where Rc= 22 miles/gallon.
Let the gas consumption rate on the highway be Rh,
where Rh= 34 miles/gallon.

Since, she has 14 gallons of gas, the distance she is able to travel depends on how many miles she covers in the city, Dc, and on the highway, which we denote Dh.

Let X be the gas she spent driving in the city.
Let 14-X be the gas she spent driving on the highway.

Clearly, Dc=22X and Dh=34(14-X).

The lower bound is limited by the distance she can travel when driving in the city alone. In this case, D_lower=14*22 miles. Similarly, the upper bound is limited by the distance that she can travel on the highway alone, D_upper=14*34.

So,    308 <= 22X+34(14-X) <= 476

Cheers.