SOLUTION: Anna can do a piece of work in 12 days. Beth can do the same work in 15 days. Charles can also do the same piece of work in 30 days. Anna starts the work and Beth joins her after 3

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Anna can do a piece of work in 12 days. Beth can do the same work in 15 days. Charles can also do the same piece of work in 30 days. Anna starts the work and Beth joins her after 3      Log On


   

Question 1157110: Anna can do a piece of work in 12 days. Beth can do the same work in 15 days. Charles can also do the same piece of work in 30 days. Anna starts the work and Beth joins her after 3 days. 3 days before the work is completed Anna leaves and Charles joins the work. In how many days will the work be completed?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You are given their rates of working:
Anna: [ 1 job ] / [ 12 days ]
Beth: [ 1 job ] / [ 15 days ]
Charles [ 1 job ] / [ 30 days ]
------------------------------------
Anna starts working alone and
works for 3 days. In 3 days she
does this fraction of the job:
+%28+1%2F12+%29%2A3+=+1%2F4+
There is +3%2F4+ of the job left
-------------------------------------
Anna and Beth then work together for
an unknown number of days.
Let +d+ = the number of days they work together
Their rate of working together is:
+1%2F12+%2B+1%2F15+=+5%2F60+%2B+4%2F60+
+1%2F12+%2B+1%2F15+=+9%2F60+
+9%2F60+=+3%2F20+
The fraction of the remaining work they get done is:
+%28+3%2F20+%29%2Ad%2A%283%2F4%29+=+%28+9%2F80+%29%2Ad+
So now +1%2F4+%2B+%28+9%2F80+%29%2Ad++ is done
+1+-+1%2F4+-+%28+9%2F80+%29%2Ad+=+3%2F4+-+%28+9%2F80+%29%2Ad+ is
the fraction left to do
---------------------------
Now for 3 days, Charles and Beth work together
and they finish the job
Add their rates of working
+1%2F15+%2B+1%2F30+=+%28+3%2F4+-+%28+9%2F80+%29%2Ad+%29+%2F+3+
+1%2F15+%2B+1%2F30+=+1%2F4+-+%28+3d+%29+%2F+80+
+2%2F30+%2B+1%2F30+=+20%2F80+-+%283d%29%2F80+
+3%2F30+=+%28+20+-+3d+%29+%2F+80+
+1%2F10+=+%28+20+-+3d+%29%2F+80+
Multiply both sides by +80+
+8+=+20+-+3d+
+3d+=+12+
+d+=+4+
So Anna and Beth worked together for +4+ days
------------------------------
Add up the days they all worked:
Anna alone: 3 days
Anna & Beth: 4 days
Charles and Beth: 3 days
+3+%2B+4+%2B+3+=+10+
They finish the work in 10 days
------------------------------------
Check my math and get a 2nd opinion if needed





Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Anna can do a piece of work in 12 days. Beth can do the same work in 15 days. Charles can also do the same piece of work in 30 days. Anna starts the work and Beth joins her after 3 days. 3 days before the work is completed Anna leaves and Charles joins the work. In how many days will the work be completed?
Anna can do the work in 12 days, or 1%2F12 of work in 1 day
Beth can do the work in 15 days, or 1%2F15 of work in 1 day
Charles can do the work in 30 days, or 1%2F30 of work in 1 day

We already know that Anna worked 3 days, alone, and that Beth and Charles worked 3 days, together.
Therefore, we just need to know how many days Anna and Beth worked together.

Let number of days Anna and Beth worked together, be T
We then get: 
matrix%281%2C3%2C+3%2F12+%2B+T%2F12+%2B+T%2F15+%2B+3%2F15+%2B+3%2F30%2C+%22=%22%2C+1%29
15 + 5T + 4T + 12 + 6 = 60 -------- Multiplying by LCD, 60
5T + 4T + 15 + 12 + 6 = 60
9T + 33 = 60
9T = 27
Time Anna and Beth worked together, or matrix%281%2C6%2C+T%2C+%22=%22%2C+27%2F9%2C+%22=%22%2C+3%2C+days%29

Days needed to complete job: 
That’s ALL!!

You can do the check, and if you do, you'll see that the entire job takes 9 days, not 10 as the other person states. 
Plus, his method is very time-consuming and complex - doesn't have to be - and most likely contain errors.