princewarrior
contestada

It takes Emily eight hours to paint her house. Mike can paint the same area in nine hours. Find how long it would take them if they worked together.


7.58 hours

15.34 hours

3.56 hours

4.24 hours

Respuesta :

absor201

It will take them 4.24 hours together to paint the area together

Step-by-step explanation:

If Emily takes eight hours to paint the area then she will paint 1/8 of the house in one hour

Similarly, if Mike can paint the same area in 9 hours, then he will paint 1/9 of the same area

Let x be the number of hours in which they will together paint the area.

If x hours are taken by them to paint the area then 1/x of the area will be painted in one hour

So,

[tex]\frac{1}{8}+\frac{1}{9}=\frac{1}{x}\\Multiplying\ both\ sides\ with\ the\ LCM\\72x\\(72x)*\frac{1}{8}+(72x)*\frac{1}{9}=72x * \frac{1}{x}\\9x+8x=72\\17x=72\\Dividing\ both\ sides\ by\ 17\\\frac{17x}{17}=\frac{72}{17}\\x=4.24\ hours[/tex]

It will take them 4.24 hours together to paint the area together

Keywords: Linear equation, Variables

Learn more about linear equations at:

  • brainly.com/question/10772025
  • brainly.com/question/10879401

#LearnwithBrainly

Answer:

It would take them 4.24 hours if they worked together.

Explanation:

We are given that

time taken by emily to paint her house = 8 hours and

time take by Mike to paint the same area = 9 hours

We have to find the time taken by them if the work together, let this be x so x will be given by,  

[tex]\frac{1}{8}+\frac{1}{9}=\frac{1}{x}[/tex]

[tex]\frac{9+8}{72}=\frac{1}{x}[/tex]

[tex]x=\frac{72}{17}[/tex]

= 4.24 hours

which is the time taken by Emily and Mike to paint the house when they do it together.

Otras preguntas