To keep in shape, Vincent exercises at a track near his home. He requires 40 minutes to do 4 laps running and 7 laps walking. In contrast, he requires 18 minutes to do 2 laps running and 3 laps walking. Assuming he maintains a consistent pace while running and while walking, how long does Vincent take to complete a lap at each pace?

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joaobezerra joaobezerra · Answer 1 · 2021-02-22T01:28:50+01:00

Answer:

He completes a lap running in 3 minutes, and walking in 4 minutes.

Step-by-step explanation:

This question can be solved by a system of equations.

I am going to say that:

x is the time needed to complete a lap running.

y is the time needed to complete a lap walking.

He requires 40 minutes to do 4 laps running and 7 laps walking.

This means that:

[tex]4x + 7y = 40[/tex]

[tex]4x = 40 - 7y[/tex]

He requires 18 minutes to do 2 laps running and 3 laps walking.

This means that

[tex]2x + 3y = 18[/tex]

Multipluing everything by 2

[tex]4x + 6y = 36[/tex]

Since [tex]4x = 40 - 7y[/tex]

[tex]40 - 7y + 6y = 36[/tex]

[tex]y = 4[/tex]

And

[tex]4x = 40 - 7y[/tex]

[tex]4x = 40 - 7*4[/tex]

[tex]4x = 12[/tex]

[tex]x = \frac{12}{4}[/tex]

[tex]x = 3[/tex]

He completes a lap running in 3 minutes, and walking in 4 minutes.