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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.A couple of friends decide to race each other. Mia can run , whereas Neil can run . Because she is slower, Mia also gets a head start of . Shortly after they start running, Neil will catch up to Mia. How long will that take? How far will Neil have to run?It will take seconds for Neil to run meters and catch up to Mia.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.A couple of friends decide to race each other. Mia can run , whereas Neil can run . Because she is slower, Mia also gets a head start of . Shortly after they start running, Neil will catch up to Mia. How long will that take? How far will Neil have to run?It will take seconds for Neil to run meters and catch up to Mia.
- Define variables: Define the variables for time and distance.Let be the time in seconds it takes for Neil to catch up to Mia.Let be the distance in meters that Neil runs to catch up to Mia.
- Write Mia's equation: Write the equation for Mia's distance.Mia's distance = Mia's speed time + head startMia's distance =
- Write Neil's equation: Write the equation for Neil's distance.Neil's distance = Neil's speed timeNeil's distance =
- Set up equations: Set up the system of equations.Since Neil catches up to Mia, their distances are equal when Neil catches up.So, we have the equation:
- Solve for t: Solve for t.Subtract from both sides of the equation:Divide both sides by :
- Calculate Neil's distance: Calculate the distance Neil runs.Using the equation for Neil's distance:
- Answer prompt: Answer the question prompt.It will take seconds for Neil to run meters and catch up to Mia.
