SOLUTION: Rick can rake leaves twice as fast as his little sister. They worked together and finished the job in 8 hours. How long would it take Rick to do the job himself? Rick's sister's p

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Rick can rake leaves twice as fast as his little sister. They worked together and finished the job in 8 hours. How long would it take Rick to do the job himself? Rick's sister's p      Log On


   

Question 734255: Rick can rake leaves twice as fast as his little sister. They worked together and finished the job in 8 hours. How long would it take Rick to do the job himself?
Rick's sister's part is 1 over 2x times 8
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get their rate working
together.
Let +r+ = Sister's rate in ( jobs / hr )
+2r+ = Rick's rate in ( jobs / hr )
given:
+r+%2B+2r+=+1%2F8+
The 1/8 means ( 1 job / 8 hrs )
+3r+=+1%2F8+
+r+=+1%2F24+
+2r+=+2%2F24+
Rick could do 2 jobs in 24 hrs, which is the same as
+2%2F24+=+1%2F12+ 1 job in 12 hrs
So, he could do the job by himself in 12 hrs
check answer:
+r+%2B+2r+=+1%2F8+
+1%2F24+%2B+1%2F12+=+1%2F8+
+1%2F24+%2B+2%2F24+=+3%2F24+
+3%2F24+=+3%2F24+
OK