Bethany Rose Williams appeared in the Bendigo Magistrates' Court on Monday where she pleaded guilty to charges including careless driving.

The driver she was racing, Harry Charles Wing, also pleaded guilty to the offences on Monday.

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The court heard police were patrolling the Bendigo area in an unmarked police car on October 17 last year.

About 7.27pm, police saw a Holden station wagon and a Ford Falcon sedan stopped at a set of lights on Arnold Street.

As the lights turned green, there was a loud sound of engines revving and the two cars accelerated.

Williams, who was driving the Holden, was nabbed driving 80km/h in the 60km/h zone.

Wing's Ford Falcon was caught travelling between 100km/h to 110km/h along the same stretch of road.

The court heard the vehicles drove through a pedestrian crossing at those speeds.

Police intercepted the pair who were not known to each other.

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Williams, who had her two-year-old son in the back seat, told officers she saw Wing take off and thought she would "go for it".

She told police she was annoyed that her "piece of s*** couldn't go fast enough".

Wing also admitted to drag racing and told police "it just sort of happened".

Magistrate Rodney Higgins said their decision to drag race was "stupid" but he wouldn't disqualify them from driving.

Williams was instead convicted and fined $500, while Wing was fined $750 with conviction.

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