SOLUTION: If Greg and Nico do a 200-piece together, they can on the average complete it in 3/8 hour. On the other hand, it would take an average of 3/7 hour for Greg and Kiefer to do a simil

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If Greg and Nico do a 200-piece together, they can on the average complete it in 3/8 hour. On the other hand, it would take an average of 3/7 hour for Greg and Kiefer to do a simil      Log On


   

Question 765329: If Greg and Nico do a 200-piece together, they can on the average complete it in 3/8 hour. On the other hand, it would take an average of 3/7 hour for Greg and Kiefer to do a similar puzzle. And if all three of them work together on the average they can complete this puzzle in 15 minutes. What is the average time it would take each player to complete this puzzle?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let Greg's rate of working = +r%5Bg%5D+
Let Nico's rate of working = +r%5Bn%5D+
Let Kiefer's rate of working = +r%5Bk%5D+
-------------------------------
(1) +r%5Bg%5D+%2B+r%5Bn%5D+=+1+%2F%28%283%2F8%29%29+
(2) +r%5Bg%5D+%2B+r%5Bk%5D+=+1+%2F+%28%283%2F7%29%29+
(3) +r%5Bg%5D+%2B+r%5Bn%5D+%2B+r%5Bk%5D+=+1+%2F+%28%281%2F4%29%29+
---------------------------------
(1) +r%5Bg%5D+%2B+r%5Bn%5D+=+8%2F3+
(2) +r%5Bg%5D+%2B+r%5Bk%5D+=+7%2F3+
(3) +r%5Bg%5D+%2B+r%5Bn%5D+%2B+r%5Bk%5D+=+12%2F3+
----------------------------
Substitute (1) into (3)
(3) +8%2F3+%2B+r%5Bk%5D+=+12%2F3+
(3) +r%5Bk%5D+=+4%2F3+
and
(2) +r%5Bg%5D+%2B+4%2F3+=+7%2F3+
(2) +r%5Bg%5D+=+1+
and
(1) +3%2F3+%2B+r%5Bn%5D+=+8%2F3+
(1) +r%5Bn%5D+=+5%2F3+
-------------------
(2) +r%5Bg%5D+=+1+
(2) +r%5Bg%5D+=+1%2F1+
and
(1) +r%5Bn%5D+=+1+%2F+3%2F5+
and
(3) +r%5Bk%5D+=+1+%2F+3%2F4+
-------------------
Greg takes 1 hr to complete puzzle
Nico takes 36 minutes to complete puzzle ( +%283%2F5%29%2A60+=+36+ )
Keifer takes 45 minutes to complete puzzle