SOLUTION: Anne, Bella and Cindy can do a piece of work in 20, 30 and 60 days respectively. a) In how many days can Anne do the work if she is assisted by Bella and Cindy on every third day?
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-> SOLUTION: Anne, Bella and Cindy can do a piece of work in 20, 30 and 60 days respectively. a) In how many days can Anne do the work if she is assisted by Bella and Cindy on every third day?
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Question 1174722: Anne, Bella and Cindy can do a piece of work in 20, 30 and 60 days respectively. a) In how many days can Anne do the work if she is assisted by Bella and Cindy on every third day? Found 3 solutions by ikleyn, greenestamps, MathTherapy:Answer by ikleyn(52748) (Show Source):
Instead of solving the equation
+ + = 1,
you need to solve
+ + = 1.
Using the common denominator of 360, you get then
+ + = 1,
or
= 1
= 1
t = 15.
ANSWER. In 15 days.
We have to be careful with this. It might be that the job can be completed a day earlier if Bella and Cindy both help Anne on the first day than if they first help her on the second or third day.
On days when Anne works alone, 1/20 of the job is completed.
On days when Bella and Cindy help, the fraction of the job that gets done is 1/20 + 1/30 + 1/60 = 3/60 + 2/60 + 1/60 = 6/60 = 1/10.
So in every 3-day period, the fraction of the job that gets done is 2(1/20)+1/10 = 2/10 = 1/5.
That means the whole job will be completed in 5*3 = 15 days.
So it turns out not to matter which is the first day that Bella and Cindy help Anne.
CHECK:
Anne in 15 days does 15/20 = 3/4 of the job.
Bella in 15 days works 5 days, doing 5/30 = 1/6 of the job.
Cindy in 15 days works 5 days doing 5/60 = 1/12 of the job.
