SOLUTION: Two pipes together can fill a tank of water in 6 hours one of them takes 5 hours less than the other to fill it working alone. Find the time each will take to fill the tank.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Two pipes together can fill a tank of water in 6 hours one of them takes 5 hours less than the other to fill it working alone. Find the time each will take to fill the tank.      Log On


   

Question 725146: Two pipes together can fill a tank of water in 6 hours one of them takes 5 hours less than
the other to fill it working alone. Find the time each will take to fill the tank.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of filling
Let +t+ = time in hrs for the slowest pipe to fill tank
+t+-+5+ = time in hrs for the faster pipe to fill tank
given:
( 1 tank filled / t hrs ) + ( 1 tank filled / t - 5 hrs ) = ( 1 tank filled / 6 hrs )
+1%2Ft+%2B+1%2F%28+t+-+5+%29+=+1+%2F+6+
Multiply both sides by +6t%2A%28+t+-+5+%29+
+6%2A%28+t+-+5+%29+%2B+6t+=+t%2A%28+t+-+5+%29+
+6t+-+30+%2B+6t+=+t%5E2+-+5t+
+t%5E2+-+17t+%2B+30+=+0+
+%28+t+-+15+%29%2A%28+t+-+2+%29+ ( just by looking at it )
I get
+t+=+15+ hrs and
+t+=+2+ hrs
It can't be +t+=+2+ because I have to subtract 5 hrs for the slower pipe
and then I get a negative.
So, +t+=+15+ and
+t+-+5+=+10+
The slower pipe fills in 15 hrs
The faster pipe fills in 10 hrs
check:
+1%2Ft+%2B+1%2F%28+t+-+5+%29+=+1+%2F+6+
+1%2F15+%2B+1%2F%28+15+-+5+%29+=+1+%2F+6+
+1%2F15+%2B+1%2F10+=+1%2F6+
+2%2F30+%2B+3%2F30+=+5%2F30+
+5%2F30+=+5%2F30+
OK