Answer
My brother's claim is incorrect
Work Step by Step
Since the gas tank holds a total of $13.5$ gallons of gas, and the gauge indicates that the tank is one-quarter full, then the amount of gas in the tank is
$$
13.5\div4=3.375\text{ gallons}
.$$
Since the car gets an average of $25$ miles per gallon, then the distance that can be covered by the car with its remaining gas is
$$\begin{aligned}
&3.375\text{ gallons} \times \frac{25\text{ miles}}{\text{gallon}}
\\&=
84.375\text{ miles}
.\end{aligned}
$$
Since the destination is $85$ miles away and
$$
84.375<85
,$$ there is not enough gas to reach the destination. Hence, my brother's claim is incorrect.
