one pipe can fill a tank in 8 hrs another pipe fill that tank in 6hrs if they open together in what time they fill tank
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Answer:
15 hours and 12 hours
Let the pipes can fill the cistern in
x
hours and
(
x
−
3
)
hours respectively
Then the part of the tank filled by the pipes in 1 hr are
1
x
and
1
x
−
3
respectively
Part of the tank filled by both pipes together in 1 hr
=
1
x
+
1
x
−
3
⋯
(
1
)
Time taken for both the pipes to fill the cistern = 6 hrs and 40 min
=
6
40
60
=
6
2
3
=
20
3
hour
Therefore, part of the tank filled by both pipes together in 1 hr =
3
20
⋯
(
2
)
From(1) and (2)
1
x
+
1
x
−
3
=
3
20
20
(
x
−
3
)
+
20
x
=
3
x
(
x
−
3
)
[∵ Multiplied both sides with
20
x
(
x
−
3
)
]
40
x
−
60
=
3
x
2
−
9
x
3
x
2
−
49
x
+
60
=
0
x
=
49
±
√
(
−
49
)
2
−
4
×
3
×
60
6
=
49
±
√
1681
6
=
49
±
41
6
=
15
or
1.33
Cannot take
x
=
1.33
because
(
x
−
3
)
will be negative.
Therefore,
x
=
15
The pipes can fill the cistern in 15 hours and 15 - 3 = 12 hours respectively
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