SOLUTION: A and B can finished one piece of work in 12days. B and C finishes in 15 days. C and A finishes it in 20 days. how may days to finish same work altogether?

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Question 630000: A and B can finished one piece of work in 12days. B and C finishes in 15 days. C and A finishes it in 20 days. how may days to finish same work altogether?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working
Let A's rate = +a+ ( 1 finished job ) / ( days to finish it )
Let B's rate = +b+ ( 1 finished job ) / ( days to finish it )
Let C's rate = +c+ ( 1 finished job ) / ( days to finish it )
given:
(1) +a+%2B+b+=+1%2F12+ ( 1 job finished ) / ( 12 days )
(2) +b+%2B+c+=+1%2F15+ ( 1 job finished ) / ( 15 days )
(3) +a+%2B+c+=+1%2F20+ ( 1 job finished ) / ( 20 days )
-----------------
Now if I add (1) and (2)
(1) +a+%2B+b+=+1%2F12+
(2) +b+%2B+c+=+1%2F15+
+a+%2B+c+%2B+2b+=+1%2F12+%2B+1%2F15+
+a+%2B+c+%2B+2b+=+5%2F60+%2B+4%2F60+
+a+%2B+c+%2B+2b+=+9%2F60+
+a+%2B+c+%2B+2b+=+3%2F20+
Subtract (3) from this
+a+%2B+c+%2B+2b+=+3%2F20+
+-a+-c+=+-1%2F20+
+2b+=+2%2F20+
+b+=+1%2F20+
Plug this into (1)
(1) +a+%2B+1%2F20+=+1%2F12+
(1) +a+=+1%2F12+-+1%2F20+
(1) +a+=+5%2F60+-+3%2F60+
(1) +a+=+2%2F60+
(1) +a+=+1%2F30+
Now plug +b+=+1%2F20+ into (2)
(2) +1%2F20+%2B+c+=+1%2F15+
(2) +c+=+1%2F15+-+1%2F20+
(2) +c+=+4%2F60+-+3%2F60+
(2) +c+=+1%2F60+
-------------------
Let +x+ = number of days to finish job
job with A,B, and C working together
+1%2F30+%2B+1%2F20+%2B+1%2F60+=+1%2Fx+
Multiply both sides by +60x+
+2x+%2B+3x+%2B+x+=+60+
+6x+=+60+
+x+=+10+
It takes them 10 days working together
to finish job
check:
(1) +a+%2B+b+=+1%2F12+
(1) +1%2F30+%2B+1%2F20+=+1%2F12+
(1) +2%2F60+%2B+3%2F60+=+5%2F60+
OK
You can check (2) and (3)