if a fire truck is pumping water at a rate of 200 L/min, how long will it take to put out a fire in a room with a floor area of 140m squared

Respuesta :

Answer:

[tex]1.09\ min[/tex]

Step-by-step explanation:

step 1

Find the minimum volume of water needed to fight a room with a floor area of 140 m^2

see the attached table to better understand the problem

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

Let

x ----> the floor area in square feet

y ---> minimum volume of water in liters

In this problem the relationship between the variables x and y represent a direct variation

Find the constant of proportionality k

Looking at the table

For x=25, y=39

[tex]k=y/x[/tex] ---->[tex]k=\frac{39}{25}=1.56[/tex]

The equation is

[tex]y=1.56x[/tex]

For x=140 m^2

substitute and solve for y

[tex]y=1.56(140)[/tex]

[tex]y=218.4\ L[/tex]

step 2

How long will it take to put out a fire in a room with a floor area of 140 m^2

we know that

The fire truck is pumping water at a rate of 200 L/min

The minimum volume of water needed is 218.4 L

so

Divide the minimum volume of water needed by the rate

[tex]218.4/200= 1.092\ min[/tex]

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