Pregunta
Write a system of equations to describe the situation below, solve using elimination, and fill in
the blanks.
To keep in shape, Miranda exercises at a track near her home. She requires 26 minutes to do
6 laps running and 5 laps walking. In contrast, she requires 34 minutes to do 10 laps running
and 6 laps walking. Assuming she maintains a consistent pace while running and while
walking, how long does Miranda take to complete a lap?
Miranda takes
Submit
the blanks.
To keep in shape, Miranda exercises at a track near her home. She requires 26 minutes to do
6 laps running and 5 laps walking. In contrast, she requires 34 minutes to do 10 laps running
and 6 laps walking. Assuming she maintains a consistent pace while running and while
walking, how long does Miranda take to complete a lap?
Miranda takes
Submit
Ask by Donnelly Pierce. in the United States
Dec 16,2024
Solución de inteligencia artificial de Upstudy
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Miranda takes 1 minute to complete a lap.
Solución

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Como
Extra Insights
Let’s define the variables: let
be the time in minutes it takes Miranda to complete one lap running, and
be the time in minutes it takes her to complete one lap walking.
From the information provided, we can set up the following system of equations:
-
For the first situation:
-
For the second situation:
Now, we will solve this system using elimination.
First, let’s align the equations for easier elimination. We’ll multiplying the first equation by 2 to align coefficients of
:
-
(this is 2 times the first equation) -
Now, we’ll multiply the second equation by 5/3 to allow for easy elimination between the
terms:
Now we can eliminate
by subtracting these equations:
This simplifies to
.
Now, combine the like terms:
This will lead us to find
and, subsequently,
.
Once you perform the calculations, you will find
and
, which lead to the final answer.
Miranda takes approximately ________ minutes to complete a lap running and ________ minutes to complete a lap walking.
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