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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Wayne and Eddie got in trouble at football practice and have to run laps as a consequence. Wayne, who runs at a rate of laps per minute, had completed laps already when he was joined on the track by Eddie. Eddie's pace is laps per minute. At some point, the two will have run the same distance. How many laps will each boy have run? How long will that take?Wayne and Eddie will each have run laps in minutes.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Wayne and Eddie got in trouble at football practice and have to run laps as a consequence. Wayne, who runs at a rate of laps per minute, had completed laps already when he was joined on the track by Eddie. Eddie's pace is laps per minute. At some point, the two will have run the same distance. How many laps will each boy have run? How long will that take?Wayne and Eddie will each have run laps in minutes.
- Define variables: Let's define the variables.Let be the number of minutes Eddie runs.Since Wayne has already completed laps and runs at a rate of laps per minute, the total laps Wayne will have run is .Eddie runs at a rate of laps per minute, so the total laps Eddie will have run is .
- Write equations: Write a system of equations to represent the situation.Wayne's laps: Eddie's laps: They will have run the same number of laps when .
- Solve equation: Solve the equation for .Subtract from both sides to isolate on one side:
- Calculate laps: Calculate the number of laps each boy will have run.Wayne's laps: Eddie's laps:
- Answer prompt: Answer the question prompt.Wayne and Eddie will each have run laps in minutes.
