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Sara leaves home at 8:00 a.m. and drives at an average speed of 45 miles per hour. Her brother Pedro leaves home at 9:00 a.m. and drives along the same path at an average speed of 65 miles per hour. a. How many hours will Sara have driven when Pedro catches up with her? hours b. How far from home are they when Pedro catches up with Sara?

Respuesta :

Using linear functions, we have that:

a. Sara will have driven 2.25 hours when Pedro catches up with her.

b. They are 146.25 miles from home when Pedro catches up with Sara.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

We have to consider the starting time as when Pedro leaves, when Sara will be at position 45 miles. Considering the velocities as the slope, the functions are:

  • S(t) = 45 + 45t.
  • P(t) = 65t.

Pedro will catch up with Sara when:

P(t) = S(t)

Hence:

65t = 45t + 45

20t = 45

t = 45/20

t = 2.25 hours.

Sara will have driven 2.25 hours when Pedro catches up with her.

The distance from home will be given by:

P(2.25) = S(2.25) = 65(2.25) = 45(2.25) + 45 = 146.25.

They are 146.25 miles from home when Pedro catches up with Sara.

More can be learned about linear functions at https://brainly.com/question/24808124

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