SOLUTION: Of three workmen, the second and third can complete a job in 10 days. The first and third can do it in 12 days, while the first and second can do it in 15 days. In how many days ca

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Of three workmen, the second and third can complete a job in 10 days. The first and third can do it in 12 days, while the first and second can do it in 15 days. In how many days ca      Log On


   

Question 857185: Of three workmen, the second and third can complete a job in 10 days. The first and third can do it in 12 days, while the first and second can do it in 15 days. In how many days can each of them do the job alone? I set up the problem like this:
10/b+10/c=1
12/a+12c=1
15/a+15/b=1
Found 3 solutions by DrBeeee, richwmiller, josmiceli:
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Your equations are correct, all we need to do is solve for a,b,c. Rewrite your equations as
(1) 1/b + 1/c = 1/10
(2) 1/a + 1/c = 1/12
(3) 1/a + 1/b = 1/15
Now subtract (3) from (2) and get
(4) (1/a + 1/c) - (1/a + 1/b) = 1/12 - 1/15 or
(5) 1/c - 1/b = (15-12)/(12*15) or
(6) 1/c - 1/b = 3/(12*15) or
(7) 1/c - 1/b = 1/60
Now add (7) and (1) to get
(8) 2/c = 1/10 + 1/60 or
(9) 2/c = 70/600 or
(10) 1/c = 7/120 or
(11) c = 120/7
Now put (10) into (1) and get
(12) 1/b + 7/120 = 1/10 or
(13) 1/b = 12/120 - 7/120 or
(14) 1/b = 5/120 or
(15) 1/b = 1/24 or
(16) b = 24
Now put (10) into (2) and get
(17) 1/a + 7/120 = 1/12 or
(18) 1/a = 10/120 - 7/120 or
(19) 1/a = 3/120 or
(20) 1/a = 1/40 or
(21) a = 40
Let's check the answer using (3).
Is (1/40 + 1/24 = 1/15)?
Is (3/120 + 5/120 = 1/15)?
Is (8/120 = 1/15)?
Is (2/30 = 1/15)?
Is (1/15 = 1/15)? Yes
Answer: a = 40, b = 24 and c = 120/7




Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
10/b+10/c=1,
12/a +12/c=1,
15/a+15/b=1
1/b +1/c=1/10
1/a +1/c=1/12
1/a+1/b =1/15
a = 40, b = 24, c = 120/7

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the rates that the 3 workmen work in
( jobs completed ) / ( days to complete them ) =
+R%5B1%5D+, +R%5B2%5D+, and +R%5B3%5D+
given:
(1) +R%5B2%5D+%2B+R%5B3%5D+=+1%2F10+
(2) +R%5B1%5D+%2B+R%5B3%5D+=+1%2F12+
(3) +R%5B1%5D+%2B+R%5B2%5D+=+1%2F15+
------------------------
Subtract (3) from (2)
(2) +R%5B1%5D+%2B+R%5B3%5D+=+1%2F12+
(3) +-R%5B1%5D+-+R%5B2%5D+=+-1%2F15+
------------------------
+R%5B3%5D+-+R%5B2%5D+=+1%2F12+-+1%2F15+
Add this result to (1)
+-R%5B2%5D+%2B+R%5B3%5D+=+1%2F12+-+1%2F15+
(1) +R%5B2%5D+%2B+R%5B3%5D+=+1%2F10+
+2%2AR%5B3%5D+=+1%2F10+%2B+1%2F12+-+1%2F15+
+R%5B3%5D+=+1%2F20+%2B+1%2F24+%2B+1%2F30+
+R%5B3%5D+=+12%2F240+%2B+10%2F240+%2B+8%2F240+
+R%5B3%5D+=+30%2F240+
+R%5B3%5D+=+1%2F8+
The 3rd, working alone can do
the job in 8 days
You can find +R%5B1%5D+ and +R%5B2%5D+