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Anna and Elsa are helping set up for the Christmas celebration at Magic Kingdom. They have to install 7 million lights for the annual display. It takes Elsa 14 days to set up the 7 million lights by herself and it takes Anna 11 days to set up the 7 million lights by herself. How long will it take them to do it together?

Respuesta :

Answer:

If they work together, they will take 6.16 days.

Step-by-step explanation:

Elsa takes 14 days to complete the work.

So, 1 day work by Elsa is [tex]\frac{1}{14}[/tex]

Anna takes 11 days to complete the work.

So, 1 day work by Anna is [tex]\frac{1}{11}[/tex].

So, Let if they work together, it would take x number of days.

So, we can set up equation as

[tex]\frac{1}{14} +\frac{1}{11}=\frac{1}{x}[/tex]

Find LCD, which is 154.

[tex]\frac{11}{154} +\frac{14}{154} =\frac{1}{x}[/tex]

Simplify

[tex]\frac{25}{154} =\frac{1}{x}[/tex]

Cross multiply,

25x=154

Divide both sides by 25

x=6.16 days

If they work together, they will take 6.16 days.

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