SOLUTION: When Sammi and Lamore work together, they can deliver flyers to all the homes in their neighborhood in 24 min. When Lamore works alone, he needs 14 minutes longer to deliver flyers

Algebra ->  Rate-of-work-word-problems -> SOLUTION: When Sammi and Lamore work together, they can deliver flyers to all the homes in their neighborhood in 24 min. When Lamore works alone, he needs 14 minutes longer to deliver flyers      Log On


   

Question 927538: When Sammi and Lamore work together, they can deliver flyers to all the homes in their neighborhood in 24 min. When Lamore works alone, he needs 14 minutes longer to deliver flyers than Sammi when she works alone. When Sammi works alone, how long does she take to deliver the flyers?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +1%2Ft+ = Sammi's rate of delivering
in jobs / minutes
+1+%2F+%28+t+%2B+14+%29+ = Lamore's rate of delivering
in jobs / minutes
----------------------
Add their rates of delivering to get their
rate working together
----------------------
+1%2Ft+%2B+1%2F%28+t+%2B+14+%29+=+1%2F24+
Multiply both sides by +24%2At%2A%28+t+%2B+14+%29+
+24%2A%28+t%2B14+%29+%2B+24t+=+t%2A%28+t%2B14+%29+
+24t+%2B+336+%2B+24t+=+t%5E2+%2B+14t+
+t%5E2+-+48t+%2B+14t+-+336+=+0+
+t%5E2+-+34t+-+336+=+0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-34+
+c+=+-336+
+t+=+%28+-%28-34%29+%2B-+sqrt%28+%28-34%29%5E2+-+4%2A1%2A%28-336%29+%29%29+%2F+%282%2A1%29+
+t+=+%28+34+%2B-+sqrt%28+1156+%2B+1344+%29%29+%2F+2+
+t+=+%28+34+%2B+sqrt%28+2500+%29+%29+%2F+2+
+t+=+%28+34+%2B+50+%29+%2F+2+ ( can't use the negative sqrt )
+t+=+84%2F2+
+t+=+42+
Sammi takes 42 min working alone
----------------
check:
+t+%2B+14+=+56+ min
+1%2Ft+%2B+1%2F%28+t+%2B+14+%29+=+1%2F24+
+1%2F42+%2B+1%2F%28+42+%2B+14+%29+=+1%2F24+
+1%2F42+%2B+1%2F56+=+1%2F24+
+1%2F21+%2B+1%2F28+=+1%2F12+
+.04762+%2B+.03571+=+.08333+
+.08333+=+.08333+
OK