Question

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?

Answer 1

If they work together, they will take 6.16 days.

Explanation:

Elsa takes 14 days to complete the work.

So, 1 day work by Elsa is
`(1)/(14)`

Anna takes 11 days to complete the work.

So, 1 day work by Anna is
`(1)/(11)`.

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

So, we can set up equation as

`(1)/(14) +(1)/(11)=(1)/(x)`

Find LCD, which is 154.

`(11)/(154) +(14)/(154) =(1)/(x)`

Simplify

`(25)/(154) =(1)/(x)`

Cross multiply,

25x=154

Divide both sides by 25

x=6.16 days

If they work together, they will take 6.16 days.