SOLUTION: It takes an apprentice twice as long as the experienced plumber to replace the pipes under an old house. If it takes them 5 hours when they work together, how long would it take th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes an apprentice twice as long as the experienced plumber to replace the pipes under an old house. If it takes them 5 hours when they work together, how long would it take th      Log On


   

Question 961638: It takes an apprentice twice as long as the experienced plumber to replace the pipes under an old house. If it takes them 5 hours when they work together, how long would it take the apprentice alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hours
+1%2Ft+ = the experienced plumber's
rate of working
+1%2F%282t%29+ = the apprentice's rate of working
--------------------
Add their rates to get their rate
working together
+1%2Ft+%2B+1%2F%282t%29+=+1%2F5+
Multiply both sides by +10t+
+10+%2B+5+=+2t+
+2t+=+15+
+t+=+7.5+
-------------
The apprentice, working alone, takes 15 hrs
check:
+1%2Ft+%2B+1%2F%282t%29+=+1%2F5+
+1%2F7.5+%2B+1%2F15+=+1%2F5+
+2%2F15+%2B+1%2F15+=+3%2F15+
+3%2F15+=+3%2F15+
OK