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22990atinesh
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Homework Statement
Q. A cistern has 3 pipes X, Y, Z. X and Y are filler pipes used in filling the tank in 4 & 5 hours respectively. Z is an exhaust pipe which empties the tank in 2 hours. If the pipes are opened in order at 4 AM, 5 AM & 6 AM respectively. Then When will the cistern become empty ?
Homework Equations
The Attempt at a Solution
##R_X## Rate of pipe X = ##\frac {1}{4}##
##R_Y## Rate of pipe Y = ##\frac {1}{5}##
##R_Z## Rate of pipe Z = ##\frac {1}{2}##
X --> 4 AM --> t
Y --> 5 AM --> t+1
Z --> 6 AM --> t+2
"Cistern become Empty" represents 0 work
##t*R_X## + ##(t+1)*R_Y## + ##(t+2)*R_Z## = 0
##t=14 hours => 8 PM##
Is it the correct answer and does my approach is correct. If anybody has a more simpler approach then please share...