Bike path

Bill was riding his bike on a bike path that was 5 1/4 miles long. He rode his bike awhile and stopped for s drink or water. Then he rode 2 7/10 miles and was at the end of the path. How far had Bill ridden before he stopped for water?

Correct answer:

x =  2 ¹¹⁄₂₀ = 51/20 mi

Step-by-step explanation:

$$\begin{gathered} a=5\frac{1}{4}=5+\frac{1}{4}=\frac{5\cdot 4+1}{4}=\frac{20+1}{4}=\frac{21}{4}=5.25\text{mi} \\ b=2\frac{7}{10}=2+\frac{7}{10}=\frac{2\cdot 10+7}{10}=\frac{20+7}{10}=\frac{27}{10}=2.7\text{mi} \\ x=a-b=\frac{21}{4}-\frac{27}{10}=\frac{105}{20}-\frac{54}{20}=\frac{105-54}{20}=\frac{51}{20}=\frac{51}{20}\text{mi}=2\frac{11}{20}\text{mi}=2.55\text{mi} \end{gathered}$$

Try another example