SOLUTION: Pat and Jen volunteer at the library. Pat can shelve a full cart of books 14 minutes faster than Jen. If they work together, they can shelve a full cart in 24 minutes. How long doe

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Question 945299: Pat and Jen volunteer at the library. Pat can shelve a full cart of books 14 minutes faster than Jen. If they work together, they can shelve a full cart in 24 minutes. How long does it take Jen to shelve a full cart by herself?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Jen's time in minutes to shelve a cart
+t+-+14+ = Pat's time in minutes to shelve a cart
-------------------
Jen's rate:
( 1 cart ) / ( t min )
Pat's rate:
( 1 cart ) / ( t - 14 min )
Working together:
( 1 cart ) / ( 24 min )
----------------------
Add their rates to get rate working together
+1%2Ft+%2B+1%2F%28+t+-+14+%29+=+1%2F24+
Multiply both sides by +t%2A%28+t+-+14+%29%2A24+
+24%2A%28+t+-+14+%29+%2B+24t+=+t%2A%28+t+-+14+%29+
+24t+-+336+%2B+24t+=+t%5E2+-+14t+
+t%5E2+-+62t+%2B+336+
-------------------
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-62+
+c+=+336+
+t+=+%28+-%28-62%29+%2B-+sqrt%28+%28-62%29%5E2+-+4%2A1%2A336+%29%29+%2F+%282%2A1%29+
+t+=+%28+62+%2B-+sqrt%28+3844+-+1344+%29%29+%2F+2+
+t+=+%28+62+%2B-+sqrt%28+2500+%29%29+%2F+2+
+t+=+%28+62-+50+%29+%2F+2+
+t+=+6+
( this answer makes no sense, because it is faster than
their time working together- 24 min )
+t+=+%28+62+%2B+50+%29+%2F+2+
+t+=+112%2F2+
+t+=+56+
Working alone, Jen's time is 56 sec
--------------------------------
check:
+1%2Ft+%2B+1%2F%28+t+-+14+%29+=+1%2F24+
+1%2F56+%2B+1%2F42+=+1%2F24+
+1%2F28+%2B+1%2F21+=+1%2F12+
+252%2F7056+%2B+336%2F7056+=+588%2F7056+
+588+=+588+
OK