SOLUTION: Charlie can paint a house in 16 hours. He hires a partner so that working together they can paint a house in 10 hours. If charlie gets ill, how long will it take his partner to pai

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Charlie can paint a house in 16 hours. He hires a partner so that working together they can paint a house in 10 hours. If charlie gets ill, how long will it take his partner to pai      Log On


   

Question 891568: Charlie can paint a house in 16 hours. He hires a partner so that working together they can paint a house in 10 hours. If charlie gets ill, how long will it take his partner to paint the house by himself?
Found 2 solutions by nerdybill, josmiceli:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Charlie can paint a house in 16 hours. He hires a partner so that working together they can paint a house in 10 hours. If charlie gets ill, how long will it take his partner to paint the house by himself?
.
Let x = time (hours) it takes for partner alone
then
10(1/16 + 1/x) = 1
multiplying both sides by 16x we get:
10(x + 16) = 16x
10x + 160 = 16x
160 = 6x
160/6 = x
26.667 = x
or
26 hours and 40 minutes = x (answer)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of painting to get their rate
painting together
Charlie's rate:
( 1 house ) / ( 16 hours )
Let +t+ = time in hours for the partner
to painty the house
Partner's rate:
( 1 house ) / ( t hours )
------------------------
+1%2F16+%2B+1%2Ft+=+1%2F10+
Multiply both sides by +80t+
+5t+%2B+80+=+8t+
+3t+=+80+
+t+=+26.667+
+.667%2A60+=+40+
The partner will take 26 hours and 40 minutes
working alone