SOLUTION: Can't solve this question please help. - Abby, Barry and Crystal are artists painting a mural. Working together it takes them 6 days to complete the entire painting. While worki

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Can't solve this question please help. - Abby, Barry and Crystal are artists painting a mural. Working together it takes them 6 days to complete the entire painting. While worki      Log On


   

Question 882375: Can't solve this question please help.
- Abby, Barry and Crystal are artists painting a mural. Working together it takes them 6 days to complete the entire painting. While working, they notice that Abby paints 3 times faster than Crystal, and Barry paints 1.5 times faster than Crystal. How long would it have taken Crystal to paint the mural alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get
their rate working together
Let +R%5BA%5D+ = Abby's rate
Let +R%5BB%5D+ = Barry's rate
Let +R%5BC%5D+ = Crystal's rate
Their rate working together is
( 1 mural ) / ( 6 days ), so
(1) +R%5BA%5D+%2B+R%5BB%5D+%2B+R%5BC%5D+=+1%2F6+
Also given:
(2) +R%5BA%5D+=+3%2AR%5BC%5D+
(3) +R%5BB%5D+=+1.5%2AR%5BC%5D+
----------------------
Substitute (2) and (3) into (1)
(1) +3%2AR%5BC%5D+%2B+%283%2F2%29%2AR%5BC%5D+%2B+R%5BC%5D+=+1%2F6+
(1) +%2811%2F2%29%2AR%5BC%5D+=+1%2F6+
(1) +R%5BC%5D+=+2%2F66+
(1) +R%5BC%5D+=+1%2F33+
Crystal would have taken 33 days to
paint the mural working alone
----------------------------
check:
(2) +R%5BA%5D+=+3%2AR%5BC%5D+
(2) +R%5BA%5D+=+3%2A%281%2F33%29+
(2) +R%5BA%5D+=+1%2F11+
and
(3) +R%5BB%5D+=+1.5%2AR%5BC%5D+
(3) +R%5BB%5D+=+%283%2F2%29%2A%281%2F33%29+
(3) +R%5BB%5D+=+1%2F22+
---------------------
and, from (3):
(1) +R%5BA%5D+%2B+R%5BB%5D+%2B+R%5BC%5D+=+1%2F6+
(1) +1%2F11+%2B+1%2F22+%2B+1%2F33+=+1%2F6+
(1) +6%2F66+%2B+3%2F66+%2B+2%2F66+=+1%2F6+
(1) +11%2F66+=+1%2F6+
(1) +1%2F6+=+1%2F6+
OK