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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTo keep in shape, Dillon exercises at a track near his home. He requires 5050 minutes to do 1010 laps running and 55 laps walking. In contrast, he requires 4747 minutes to do 99 laps running and 55 laps walking. Assuming he maintains a consistent pace while running and while walking, how long does Dillon take to complete a lap?\newlineDillon takes _\_ minutes to run a lap and _\_ minutes to walk a lap.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTo keep in shape, Dillon exercises at a track near his home. He requires 5050 minutes to do 1010 laps running and 55 laps walking. In contrast, he requires 4747 minutes to do 99 laps running and 55 laps walking. Assuming he maintains a consistent pace while running and while walking, how long does Dillon take to complete a lap?\newlineDillon takes _\_ minutes to run a lap and _\_ minutes to walk a lap.
  1. Define Lap Times: Let's denote the time it takes Dillon to run a lap as rr minutes and the time it takes to walk a lap as ww minutes. We are given that 1010 laps running and 55 laps walking take 5050 minutes, which gives us the equation 10r+5w=5010r + 5w = 50.
  2. Form Equations: Similarly, we are given that 99 laps running and 55 laps walking take 4747 minutes, which gives us the equation 9r+5w=479r + 5w = 47.
  3. Eliminate Variable: We now have a system of two equations. We need to eliminate one of the variables, rr or ww. We choose to eliminate ww because its coefficients are the same in both equations.
  4. Solve for rr: To eliminate ww, we can subtract the second equation from the first equation. This gives us 10r+5w−(9r+5w)=50−4710r + 5w - (9r + 5w) = 50 - 47, which simplifies to r=3r = 3.
  5. Substitute and Solve: Now that we have the value for rr, we can substitute it back into one of the original equations to solve for ww. We'll use the first equation: 10(3)+5w=5010(3) + 5w = 50, which simplifies to 30+5w=5030 + 5w = 50.
  6. Final Results: Subtracting 3030 from both sides of the equation gives us 5w=205w = 20, and dividing both sides by 55 gives us w=4w = 4.
  7. Final Results: Subtracting 3030 from both sides of the equation gives us 5w=205w = 20, and dividing both sides by 55 gives us w=4w = 4.Therefore, Dillon takes 33 minutes to run a lap and 44 minutes to walk a lap.

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