SOLUTION: Carmen's rate of solving a certain puzzle is three times that of Joseph. One day, they worked together for 40 mins, after which Joseph was called for an errand. Carmelo finished th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Carmen's rate of solving a certain puzzle is three times that of Joseph. One day, they worked together for 40 mins, after which Joseph was called for an errand. Carmelo finished th      Log On


   

Question 243126: Carmen's rate of solving a certain puzzle is three times that of Joseph. One day, they worked together for 40 mins, after which Joseph was called for an errand. Carmelo finished the rest of the puzzle in 20 minutes. How long would it take each to solve the puzzle alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Carmen's rate of solving a certain puzzle is three times that of Joseph.
One day, they worked together for 40 mins, after which Joseph was called for an errand.
Carmelo finished the rest of the puzzle in 20 minutes.
How long would it take each to solve the puzzle alone?
:
Let t = time required for Carmen to solve the puzzle alone
She works 3 times as fast as Joseph, therefore
3t = time required by Joseph to solve it alone
:
Let the completed puzzle = 1
:
Joe works for 40 min and Carm works for 40+20 = 60 min
:
60%2Ft + 40%2F%283t%29 = 1
Multiply equation by 3t, results
3(60) + 40 = 3t
180 + 40 = 3t
3t = 220
t = 220%2F3
t = 731%2F3 min for Carmen
and
5*73.33 = 220 min for Joe