#### Answer

There were 244 female runners.

#### Work Step by Step

Let $w$ be the number of women in the race.
The number of men is $w+112$.
$w+w+112=600$ $\longrightarrow$combine like terms
$2w+112=600$ $\longrightarrow$addition property
$2w+112-112=600-112$ $\longrightarrow$combine like terms
$2w=488$ $\longrightarrow$multiplication property
$2w\div2=488\div2$ $\longrightarrow$divide
$w=244$