SOLUTION: John can paint a wall in 9 days and Kyle paints the same wall in 15 days. Find out: a) how long it will take for John and Kyle to paint the wall together and b) if Kyle started pai

Algebra ->  Rate-of-work-word-problems -> SOLUTION: John can paint a wall in 9 days and Kyle paints the same wall in 15 days. Find out: a) how long it will take for John and Kyle to paint the wall together and b) if Kyle started pai      Log On


   

Question 832191: John can paint a wall in 9 days and Kyle paints the same wall in 15 days. Find out: a) how long it will take for John and Kyle to paint the wall together and b) if Kyle started painting the wall, and John joins after 5 days, how many additional days will it take them to complete the job
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
( 1 wall / 9 days ) + ( 1wall / 15 days ) = ( 1 wall / x days )
+1%2F9+%2B+1%2F15+=+1%2Fx+
Multiply both sides by +45x+
+5x+%2B+3x+=+45+
+8x+=+45+
+x+=+5.625+
They can paint the wall in 5.625 days painting together
----------------------
If Kyle paints for 5 days, I can say:
+1%2F9+=+y%2F5+
+y+=+5%2F9+
So, Kyle paints 5%2F9 of the wall in 5 days
There is +1+-+5%2F9+=+4%2F9+ of the wall left to paint
Now I can say:
+1%2F9+%2B+1%2F15+=+%284%2F9%29%2Fz+
+5z+%2B+3z+=+45%2A%284%2F9%29+
+8z+=+20+
+z+=+2.5+
It will take 2.5 more days to complete the job