A winery has a vat w/ two pipes leading to it. The inlet pipe can fill the vat i

Question

A winery has a vat w/ two pipes leading to it. The inlet pipe can fill the vat in 6 hours, while the outlet pipe can empty it in 10 hours. How long will it take to fill the vat if both pipes are left open? Then, assume that the error was discovered after both pipes have been running for 4 hours and the outlet pipe is closed. How much more time would require to fill the vat?
It will take __ hrs to fill the vat if both pipes are left open
It will take __ hrs to fill the vat after the outlet pipe is closed

Explanation / Answer

a)The first pipe fills 1/6 of the vat per hour. The 2nd pipe drains out 1/10 of the vat per hour

Total work =1/6 - 1/10
= 5/30 - 3/30
= 2/30
=1/15

So the vat is being filled by 1/15th per hour

(1/15) * t = 1
t = 15 hours

b) combined work=1/15

For 4 hours = 4/15

Remiang work 11/15 have to done only with closes pipe

Time=( 11/15 )*6

=4.4 hours

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