Question

Critique Jamie's work by explaining the reasonableness of the scenario and theaccuracy of the two parts of the graph he described. For any portion of Jamie's response in which he has made an error,provide and explain an alternative response.To enhance Jamie's explanation, describe both sections of the piecewise function using linear equations. Include any limitsto the domain.

Answer 1

From the start until minute 12, the distance elapsed is:

1/12 of a mile per minute.

As you can confirm, after 12 minutes the relay has run one mile.

From that moment, the speed changes and we have:

1/8 of a mile per minute.

As you can confirm, it takes (20 - 12) minutes to run the second mile.

Using linear equations, we have then:

x = Total distance the relay runs at a steady pace

x/12 * 12 + x/8 * 8 = 2

x + x = 2

2x = 2

x = 1

Every runner runs 1/12 or 0.083 of a mile per minute from the start until first mile, then every runner runs 1/8 or 0.125 of a mile per minute from the first mile to the second mile.

For the first mile a total of 12 runners do the relay, for the second part just 8 runners do the relay.

Jamie's work is not accurate because he says that every runner runs at a steady but faster pace (second condition stated in the information given). Actually, the speed is constant until the finish of the first mile, every runner runs at the same speed the same distance.

First linear equation:

x = Distance run by every runner

Total distance = 1 mile

Time it takes to run the first mile = 12 minutes

For solve for x, we write:

x * 12 = 1

12x = 1

x = 1/12

x = 0.083 miles

That is the distance every runner runs from the start to first mile

Now, we use the same process to solve for x: for the second equation

x = Distance run by every runner

Total distance = 1 mile

Time it takes to run the first mile = 8 minutes

For solve for x, we write:

x * 8 = 1

8x = 1

x = 1/8

x = 0.125 miles