Answer:
a. In this problem, we can let x represent the time in hours that Carson jogs after leaving school, and y represent the distance in miles that Carson is from school when he catches up with Arturo.
b. To solve for the time it will take Carson to catch up with Arturo, we can set up a system of equations that relates the distances that Arturo and Carson travel:
Distance traveled by Arturo: y + 0.2
Distance traveled by Carson: 6x
When Carson catches up with Arturo, they will have traveled the same distance, so we can set the two expressions for distance equal to each other:
y + 0.2 = 6x
We also know that the distance that Carson runs is equal to the distance that Arturo runs plus the initial distance between them, which is 0.2 miles: 6x = y + 0.2
Now we can solve the system of equations by substituting y + 0.2 for 6x in the second equation:
y + 0.2 = 6x
6x = y + 0.2
Simplifying the equations, we get:
y = 6x - 0.2
Substituting this into the first equation, we get:
6x - 0.2 + 0.2 = 0.2
Solving for x, we get:
x = 0.05 hours
To convert to minutes, we can multiply by 60:
x = 0.05 * 60 = 3 minutes
Therefore, it will take Carson 3 minutes to catch up with Arturo.