Zalmon walks 3/4 of a mile in 3/10 of an hour. What is his speed in miles per hour? А 2.3 miles per hour B 0.225 miles per hour C 2.6 miles per hourD 2.5 miles per hour



Answer :

To solve the exercise you can use a rule of three, like this

[tex]\begin{gathered} \frac{3}{4}\text{mi}\rightarrow\frac{3}{10}\text{hour} \\ x\text{ mi}\rightarrow1\text{ hour} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{1\text{ hour}\cdot\frac{3}{4}\text{ mi}}{\frac{3}{10}\text{ hour}} \\ x=\frac{1\cdot\frac{3}{4}\text{ mi}}{\frac{3}{10}} \\ x=\frac{1\cdot\frac{3}{4}}{\frac{3}{10}}\text{ mi} \\ x=\frac{\frac{3}{4}}{\frac{3}{10}}\text{ mi} \end{gathered}[/tex]

To divide fractions you operate like this

[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]

Then, you have

[tex]\begin{gathered} x=\frac{\frac{3}{4}}{\frac{3}{10}}\text{ mi} \\ x=\frac{3\cdot10}{4\cdot3}\text{ mi} \\ x=\frac{10}{4}\text{ mi} \\ x=\frac{5}{2}\text{ mi} \\ x=2.5\text{ mi} \end{gathered}[/tex]

Therefore, Zalmon's speed is 2.5 miles per hour.