one pipe can fill a tank in 3 hours less than other two pipes can fill the tank in 3 hours 36 minutes find the time each pipe would take to fill the tank
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12 hrs and 15 hrs
Let the pipe can fill the cistern be x and x−3 hours.
Two pipes together can fill the cistern in 6 hours 40 minutes =
x
1
+
x−3
1
Time taken for both the pipes to fill the cistern =6 hours 40 minutes
=6
60
40
=6
3
2
=
3
20
Therefore, part of the tank filled by both pipes together in 1 hour =
20
3
So,
x
1
+
x−3
1
=
20
3
⇒
x(x−3)
x−3+x
=
20
3
⇒
x
2
−3x
2x−3
=
20
3
⇒40x−60=3x
2
−9x
⇒3x
2
−49x+60=0
⇒3x
2
−49x+60=0
⇒
2a
−b±
b
2
−4ac
⇒
2×3
49±
(−49)
2
−4×60×3
6
49±
1681
⇒
6
49±41
⇒15 or 1.33
Cannot take x=1.33 because (x−3) will be negative.
Therefore, x=15
The pipe can fill the cistern be 15 hours and 15−3=12 hours.
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