SOLUTION: A & B together can paint a room in 18 days . they work together for 8 days and then b goes away. A finishes the rest of work in 15 days . how long would each take to finish the wor

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A & B together can paint a room in 18 days . they work together for 8 days and then b goes away. A finishes the rest of work in 15 days . how long would each take to finish the wor      Log On


   

Question 838265: A & B together can paint a room in 18 days . they work together for 8 days and then b goes away. A finishes the rest of work in 15 days . how long would each take to finish the work saperatly?
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
18/a+18/b=1,
23/a+8/b=1
a = 27, b = 54

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R%5Ba%5D+ = A's rate of painting
Let +R%5Bb%5D+ = B's rate of painting
Let +R+%5Bc%5D+ = their rate painting together
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You can add their individual rates to get their
rate working together:
+R%5Ba%5D+%2B+R%5Bb%5D+=+R%5Bc%5D+
+R%5Bc%5D+ = ( 1 room painted ) / ( 18 days )
+R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F18+
What fraction of the room do they get done in 8 days?
+x%2F8+=+1%2F18+
+18x+=+8+
+x+=+8%2F18+
+x+=+4%2F9+
The paint 4%2F9 of the room, so there is 5%2F9 left to paint
A has to finish the job, which is 5%2F9 of the room alone
given:
+R%5Ba%5D+=+%285%2F9%29%2F15+
+R%5Ba%5D+=+1%2F27+
and, since
+R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F18+
+1%2F27+%2B+R%5Bb%5D+=+1%2F18+
+R%5Bb%5D+=+1%2F18+-+1%2F27+
+R%5Bb%5D+=+3%2F54+-+2%2F54+
+R%5Bb%5D+=+1%2F54+
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A can paint the room alone in 27 days
B can paint the room alone in 54 days
check:
In the last 15 days, A gets 15/27 of the room done
12/27 has already been painted
Is this true:
+4%2F9+=+12%2F27+
+4%2F9+=+4%2F9+
OK