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Question 29587: need help plz...heres the question "There are three friends named Allan, Bobby and Charlie. The three friends want to know their individual rate in finishing a job. Allan and Bobby can finish the job in 42 days, Bobby and Charlie can finish the job in 31 days, and Allan and Charlie can finish the job in 20 days. Solve the rate of each individual."
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! need help plz...heres the question "There are three friends named Allan, Bobby and Charlie. The three friends want to know their individual rate in finishing a job. Allan and Bobby can finish the job in 42 days, Bobby and Charlie can finish the job in 31 days, and Allan and Charlie can finish the job in 20 days. Solve the rate of each individual."
LET ALLAN TAKE A DAYS TO DO THE JOB ALONE
HENCE ALLAN ALONE CAN DO IN 1 DAY 1/A JOB
LET BOBBY TAKE B DAYS TO DO THE JOB ALONE
HENCE BOBBY ALONE CAN DO IN 1 DAY 1/B JOB
LET CHARLIE TAKE C DAYS TO DO THE JOB ALONE
HENCE CHARLIE ALONE CAN DO IN 1 DAY 1/C JOB
FROM ABOVE WE GET ...
ALLAN AND BOBBY CAN DO IN 1 DAY ..1/A +1/B =(A+B)/AB JOB..
SO DAYS THEY TAKE TO COMPLETE THE JOB =AB/(A+B)=42..OR..1/A+1/B=1/42..........I BOBBY AND CHARLIE CAN DO IN 1 DAY ..1/B +1/C =(B+C)/BC JOB..
SO DAYS THEY TAKE TO COMPLETE THE JOB =BC/(B+C)=31..OR..1/B+1/C=1/31.........II
ALLAN AND CHARLIE CAN DO IN 1 DAY ..1/A +1/C =(A+C)/AC JOB..
SO DAYS THEY TAKE TO COMPLETE THE JOB =AC/(A+C)=20..OR..1/A+1/C=1/20........III
EQNI+EQNII+EQNIII GIVES...
2{(1/A)+(1/B)+(1/C)}=(1/42)+(1/31)+(1/20)
(1/A)+(1/B)+(1/C)=(1/2)*{(1/42)+(1/31)+(1/20)}.........IV
EQN.IV-EQN.I GIVES
1/C= (1/2)*{(1/42)+(1/31)+(1/20)}-1/42....OR.....C=34.2 DAYS
EQN.IV-EQN.II GIVES.......
1/A=(1/2)*{(1/42)+(1/31)+(1/20)}- 1/31...OR......A=48.1 DAYS
EQN.IV-EQN.III GIVES....
1/B=(1/2)*{(1/42)+(1/31)+(1/20)}- 1/20....OR.....B=329.6 DAYS
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