We are given that a plane covers a distance of 346 miles in 2 1/4 hours. And we are asked to determine the ratio between distance and time. To do that we will divide the total distance over the amount of time, like this:
[tex]r=\frac{346\text{miles}}{2\frac{1}{4}hour}[/tex]
Now, the time is expressed as a mixed fraction. We can rewrite it as a fraction using the following relationship:
[tex]a\frac{b}{c}=a+\frac{b}{c}[/tex]
Applying the relationship we get:
[tex]\frac{346\text{miles}}{2\frac{1}{4}hour}=\frac{346\text{miles}}{(2+\frac{1}{4})hour}[/tex]
Now, we add the fractions:
[tex]\frac{346\text{miles}}{(2+\frac{1}{4})hour}=\frac{346\text{miles}}{\frac{9}{4}\text{hour}}[/tex]
Simplifying we get:
[tex]\frac{346\text{miles}}{\frac{9}{4}\text{hour}}=\frac{4(346\text{miles)}}{9\text{hour}}=\frac{1384miles}{9hour}[/tex]
Now, solving the operation we get the unit rate:
[tex]\frac{1384miles}{9hour}=153.\bar{7}mph[/tex]
Therefore, the unit rate is 157.7 mph.
