Athletic race

Before a race, you start 4 5/8 feet behind your friend. You are 3 2/3 feet ahead of your friend at the halfway point. What is the change in distance between you and your friend from the beginning of the race?

Correct answer:

d =  8 ⁷⁄₂₄ = 199/24 ft

Step-by-step explanation:

$$\begin{gathered} a=3\frac{2}{3}=3+\frac{2}{3}=\frac{3\cdot 3+2}{3}=\frac{9+2}{3}=\frac{11}{3}\doteq 3.6667\text{ft} \\ b=4\frac{5}{8}=\frac{37}{8}=4.625\text{ft} \\ d=a+b=\frac{11}{3}+\frac{37}{8}=\frac{88}{24}+\frac{111}{24}=\frac{88+111}{24}=\frac{199}{24}=\frac{199}{24}\text{ft}=8\frac{7}{24}\text{ft}=8.2917\text{ft} \end{gathered}$$

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