Question

In a charity triathlon, Mark ran half the distance and swam a quarter of the distance. When he took a quick break to get a drink of Gatorade, he was juststarting to bike the remaining 14 miles. What was the total distance of the race?The total distance of the race wasmiles.

Answer 1

Taking the distance as d, we have that:

$\frac{1}{2}d+\frac{1}{4}d+xd=d$

In this equation, it is expressed that he ran half the distance which is 1/2d, he swam a quarter of the distance, which is 1/4d and the remaining is xd, which is how far did he ride the bike (14 miles). Solve the equation for x:

$\begin{gathered} \frac{1}{2}d+\frac{1}{4}d+xd=d \\ \frac{3}{4}d+xd=d \\ xd=d-\frac{3}{4}d \\ xd=\frac{1}{4}d \\ x=\frac{1}{4}\frac{d}{d} \\ x=\frac{1}{4} \end{gathered}$

It means that he ride the bike a quarter of the distance. We know that he ride the bike 14 miles, which means that 14 miles is a quarter of the distance, using this information we can find the total distance of the race:

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