Nakita recorded a video of homecoming highlights of the senior class and now everybody wants a copy. She promised to have 25 ready the next day but suddenly realized that it will take her ten hours to do that. Her friend, Abby, volunteered to help and she can do the job alone in 15 hours. How long will it take the girls, working together, to complete the job?

Question

Nakita recorded a video of homecoming highlights of the senior class and now everybody wants a copy.  She promised to have 25 ready the next day but suddenly realized that it will take her ten hours to do that.  Her friend, Abby, volunteered to help and she can do the job alone in 15 hours.  How long will it take the girls, working together, to complete the job?

hartnn · Answer

so, nakita can do the job in 10 hrs and 
Abby cn do it in 15 hours.

can you tell me what fraction of work, will nakita do in 1 hour ??

anonymous · Answer

I have no idea.

hartnn · Answer

its easy, 
nakita can do the job in 10 hrs
so she will do $\large 1/10 th$ of the work in 1 hour
got this ?

anonymous · Answer

Oh, okay

hartnn · Answer

what fraction of work, will abby do in 1 hour ??

anonymous · Answer

1/15

hartnn · Answer

correct, so TOGETHER in one hour , they will do 
1/10 +1/15 th fraction of the work ! right ?? 

can you simplify , 1/10 +1/15 ?

anonymous · Answer

1/6

hartnn · Answer

good! 
so 1/6 th of the work will be done in 1 hour by working together,
so in how many hours will they complete the work ??

anonymous · Answer

six hours?

hartnn · Answer

absolutely correct! 
wasn't it easy ;)

anonymous · Answer

That was way more easy than I thought.

hartnn · Answer

in general, if A can do the work in 'x' hrs, B can do the work in 'y' hrs, 
then together they will complete the work in $\large (1/x+1/y)^{-1}$ hrs.
the same thing we did here :)

hartnn · Answer

ask if any more doubts anywhere :)

anonymous · Answer

What about a question such as this? The cheerleaders at Silver Springs High School are making and selling Christmas wreaths to earn money for their trip to Orlando.  They currently have orders for 60 wreaths.  The girls divide up into groups to construct the wreaths and after making one wreath, Samantha estimates it will take her group 16 hours to make all the wreaths if they work alone.  Aleysia’s group estimates that they can make all the wreaths in 24 hours if they work alone.  How long will it take the two groups, working together, to make all 60 wreaths?
Would you do 1/16+1/24?

anonymous · Answer

@hartnn

hartnn · Answer

first do  1/16 + 1/24 
and then don't forget to take the reciprocal! 
(like we got 1/6 and we said 6 hrs)

anonymous · Answer

so I got 5/48.

anonymous · Answer

So would I then do 5/48 times 48?

hartnn · Answer

now take the reciprocal

anonymous · Answer

48/5?

hartnn · Answer

no, $\huge \dfrac{1}{\dfrac{5}{48}}=\dfrac{48}{5}$
yes!

anonymous · Answer

Huh?

hartnn · Answer

yes, reciprocal of 5/48 is 48/5 as you said, i have shown same thing
so, working together they will complete in 48/5 or 9.6 hours

anonymous · Answer

Oh! So the reciprocal is always the answer??

hartnn · Answer

yup!
$\large (1/x+1/y)^{-1}$
the -1 exponent denotes reciprocal :)

anonymous · Answer

Oh! okay! Thank you!

hartnn · Answer

welcome ^_^