# How do you determine how far Doris can travel is Doris’s truck gets 10 \frac{2}{3} miles per gallon and her tank has 5 \frac{1}{2} gallons of gas?

Sep 28, 2014

Doris' truck has mileage 10 $\frac{2}{3}$ miles per gallon of gas, which can be written as $\frac{32}{3}$ miles per gallon of gas.

Doris can drive $\frac{32}{3}$ miles using one gallon of gas.

Doris has 5 $\frac{1}{2}$ gallons of gas.

On 1 gallons she can drive $\frac{32}{3}$ miles/ gallon

On 5 gallons she can drive ( $\frac{32}{3}$ ) miles / gallon x 5 gallon

= $\left(\frac{160}{3}\right)$ mile

On 1 gallons she can drive $\frac{32}{3}$ miles/ gallon

On half a gallon she can drive ( $\frac{32}{3}$ ) miles / gallon x 0.5 gallon

= (32 x 0.5 ) / 3 = $\left(\frac{16}{3}\right)$ miles.

on 5 $\frac{1}{2}$ gallons of gas she can travel $\left(\frac{160}{3}\right)$ mile + $\left(\frac{16}{3}\right)$mile.

$\frac{160 + 16}{3}$= $\frac{176}{3}$ = 58.67 mile.