SOLUTION: A tank can be filled in 12 minutes by two pipes running simultaneously. By the larger pipe it can be filled in 10 minutes less time than by the smaller. Find the time required for

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A tank can be filled in 12 minutes by two pipes running simultaneously. By the larger pipe it can be filled in 10 minutes less time than by the smaller. Find the time required for       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 899357: A tank can be filled in 12 minutes by two pipes running simultaneously. By the larger pipe it can be filled in 10 minutes less time than by the smaller. Find the time required for each to fill it.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add the rate of filling of the 2 pipes
to get the rate for both pipes together
-------------
Rate for both pipes together:
( 1 tank filled ) / ( 12 minutes to fill it )
----------------------------------
Let +t+ = time in minutes for the
smaller pipe to fill tank
-----------------------------
Rate for smaller pipe:
( 1 tank filled ) / ( t minutes )
--------------------------
Rate for larger pipe:
( 1 tank filled ) / ( t - 10 minutes )
-------------------------------
Doing the addition:
+1%2Ft+%2B+1%2F%28+t+-+10+%29+=+1%2F12+
Multiply both sides by:
+t%2A%28+t+-+10+%29%2A12+
++12%2A%28+t-10+%29+%2B+12t++=++t%2A%28+t-10+%29++
+12t+-+120+%2B+12t+=+t%5E2+-+10t+
+t%5E2+-+34t+%2B+120+=+0+
-----------------------
Use quadratic equation:
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-34+
+c+=+120+
+t+=+%28+-%28-34%29+%2B-+sqrt%28+%28-34%29%5E2+-+4%2A1%2A120+%29%29+%2F+%282%2A1%29+
+t+=+%28+34+%2B-+sqrt%28+1156+-+480+%29%29+%2F+2+
+t+=+%28+34+%2B-+sqrt%28+676+%29%29+%2F+2+
+t+=+%28+34+%2B+26+%29+%2F+2+
+t+=+60%2F2+
+t+=+30+
------------
There is another answer:
+t+=+%28+34+-+26+%29+%2F+2+
+t+=+8%2F2+
+t+=+4+
This answer is impossible, since it's faster filling
than both pipe open together, so:
--------------------------------
+t+=+30+
+t+-+10+=+20+
The larger pipe fills the tank in 20 minutes
The smaller pipe fills the tank in 30 minutes
--------------
check:
+1%2Ft+%2B+1%2F%28+t+-+10+%29+=+1%2F12+
+1%2F30+%2B+1%2F20+=+1%2F12+
Multiply both sides by +180+
+6+%2B+9+=+15+
OK