Evan

Evan, Samuel, and Alex are doing a biking relay on the Key Biscayne Bridge. Altogether, they bike a total of 7 miles. If Evan bikes 2 1/3 of a mile and Samuel bikes 2 1/4 of a mile, what distance does Alex bike?

Final Answer:

a =  2 ⁵⁄₁₂ = 29/12 mi

Step-by-step explanation:

$$\begin{gathered} t=7\text{mi} \\ e=2\frac{1}{3}=2+\frac{1}{3}=\frac{2\cdot 3+1}{3}=\frac{6+1}{3}=\frac{7}{3}\doteq 2.3333\text{mi} \\ s=2\frac{1}{4}=2+\frac{1}{4}=\frac{2\cdot 4+1}{4}=\frac{8+1}{4}=\frac{9}{4}=2.25\text{mi} \\ a+e+s=t \\ a=t-e-s=7-\frac{7}{3}-\frac{9}{4}=\frac{29}{12}\text{mi}=2\frac{5}{12}\text{mi}=2.4167\text{mi} \end{gathered}$$

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