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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Connor and Fred got in trouble at football practice and have to run laps as a consequence. Connor, who runs at a rate of laps per minute, had completed laps already when he was joined on the track by Fred. Fred's pace is laps per minute. At some point, the two will have run the same distance. How long will that take? How many laps will each boy have run?After minutes, Connor and Fred will each have run laps.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Connor and Fred got in trouble at football practice and have to run laps as a consequence. Connor, who runs at a rate of laps per minute, had completed laps already when he was joined on the track by Fred. Fred's pace is laps per minute. At some point, the two will have run the same distance. How long will that take? How many laps will each boy have run?After minutes, Connor and Fred will each have run laps.
- Define Variables: Let's define the variables:Let be the time in minutes after Fred starts running.Let be the total number of laps Connor runs.Let be the total number of laps Fred runs.Connor's rate is laps per minute, and he has already completed laps. So, Connor's total laps can be expressed as:
- Connor's Total Laps: Fred's rate is laps per minute, and he starts from laps. So, Fred's total laps can be expressed as:
- Fred's Total Laps: We need to find the point where Connor and Fred have run the same number of laps, which means we set their total laps equal to each other:
- Set Equations Equal: Now, we solve for :
- Solve for t: Now that we have the time, we can find out how many laps each boy has run. We'll plug back into the equations for and :
- Find Laps After Minute: So, after minute, Connor and Fred will each have run laps.
