SOLUTION: andrew can paint the house 6 times as fast as Bailey and together it takes them 7 days. How long does it take each of them alone

Algebra ->  Rate-of-work-word-problems -> SOLUTION: andrew can paint the house 6 times as fast as Bailey and together it takes them 7 days. How long does it take each of them alone      Log On


   

Question 885884: andrew can paint the house 6 times as fast as Bailey and together it takes them 7 days. How long does it take each of them alone
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R%5Bb%5D+ = Bailey's rate of painting
Let +R%5Ba%5D+ = Andrew's rate of painting
given:
(1) +R%5Ba%5D+=+6%2AR%5Bb%5D+
(2) +R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F7+
( Note that +1%2F7+ means ( 1 house painted ) / ( 7 days ) )
-----------------------
Substitute (1) into (2)
(2) +6%2AR%5Bb%5D+%2B+R%5Bb%5D+=+1%2F7+
(2) +7%2AR%5Bb%5D+=+1%2F7+
(2) +R%5Bb%5D+=+1%2F49+
and
(1) +R%5Ba%5D+=+6%2A%28+1%2F49+%29+
(1) +R%5Ba%5D+=+6%2F49+
(1) +R%5Ba%5D+=+1%2F8.1667+
Bailey's rate is 1 house in 49 days
Andrew's rate is 1 house in 8.1667 days
check:
(2) +R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F7+
(2) +6%2F49+%2B+1%2F49+=+7%2F49+
(2) +7%2F49+=+7%2F49+
OK