SOLUTION: Vincent, who is half as efficient as Eric, will take 18 days to complete a task if he worked alone. If Vincent and Eric worked together, how long will they take to complete the tas

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Vincent, who is half as efficient as Eric, will take 18 days to complete a task if he worked alone. If Vincent and Eric worked together, how long will they take to complete the tas      Log On


   

Question 921405: Vincent, who is half as efficient as Eric, will take 18 days to complete a task if he worked alone. If Vincent and Eric worked together, how long will they take to complete the task?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Vincent's rate of working:
+1%2F18+ tasks / days
Eric's rate of working ( works twice as fast ):
+1%2F9+ tasks/days
-------------------
Add their rates of working to get their
rate working together
+1%2F18+%2B+1%2F9+=+1%2Ft+
where t is time in days
------------------------
Multiply both sides by +18%2A9%2At+
+9t+%2B+18t+=+18%2A9+
+27t+=+162+
+t+=+6+
It will take them 6 days working together
check:
+1%2F18+%2B+1%2F9+=+1%2Ft+
+1%2F18+%2B+1%2F9+=+1%2F6+
+1%2F18++%2B+2%2F18+=+3%2F18+
+3%2F18+=+3%2F18+
OK