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:

`(1)/(2)d+(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} (1)/(2)d+(1)/(4)d+xd=d \\ (3)/(4)d+xd=d \\ xd=d-(3)/(4)d \\ xd=(1)/(4)d \\ x=(1)/(4)(d)/(d) \\ x=(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: