Work Problems

Question

Susan, Amy and Kristin are sisters and are supposed to pick up the toy room every night before bed. If Susan is not helping, Amy and Kristin take 36 minutes to pick up the toy room. If Amy is not helping, Susan and Kristin take an hour. If Kristin is not helping, Susan and Amy talk half an hour. If they all work together, how long will it take them to pick up the toy room?

Answer 1

It takes Amy A minutes by herself, Kristin K minutes by herself and Susan S minutes by herself.

So Amy can do 1/A of the job in one minute,

and Kristin can do 1/k of the job in one minute,

and Susan can do 1/s of the job in one minute.

 

So 1/a + 1/k = 1/36

     1/s + 1/k = 1/60

     1/a + 1/s = 1/30

 

If you add these all together you'd get

2/a + 2/s + 2/k = 5/180 + 3/180 + 6/180

2/a + 2/s + 2/k = 14/180     divide by 2 to get

1/a + 1/s + 1/k = 14/360

 

So their working together takes 360/14 minutes = 25 and 5/7 minutes