MATH SOLVE

2 months ago

Q:
# DeAngelo is training for a half marathon. Today he is running 13.25 miles. He jogs for the first half hour at a rate of 5.5 miles per hour, then increases his pace to p miles per hour for 1.5 hours. Write an equation representing this situation, and complete the statement that follows.__+__ p = ___DeAngelo's rate for the last 1.5 hours of his run is ___ miles per hour.

Accepted Solution

A:

For this case, the first thing we must do is define a variable.

We have then:

p: rate in miles per hour for the last 1.5 hours

We now write the equation that models the problem.

We have then:

[tex](0.5) * (5.5) + 1.5p = 13.25 [/tex]

Rewriting we have:

[tex]2.75 + 1.5p = 13.25 [/tex]

From here, we clear the value of p.

We have then:

[tex]1.5p = 13.25 - 2.75 p = 10.5 / 1.5 p = 7[/tex]

Answer:

DeAngelo's rate for the last 1.5 hours of his run is 7 miles per hour.

We have then:

p: rate in miles per hour for the last 1.5 hours

We now write the equation that models the problem.

We have then:

[tex](0.5) * (5.5) + 1.5p = 13.25 [/tex]

Rewriting we have:

[tex]2.75 + 1.5p = 13.25 [/tex]

From here, we clear the value of p.

We have then:

[tex]1.5p = 13.25 - 2.75 p = 10.5 / 1.5 p = 7[/tex]

Answer:

DeAngelo's rate for the last 1.5 hours of his run is 7 miles per hour.