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A certain tank can be filled by one supply pipe in 3 hours and by a second supply pipe in 4 hours. The tank can be drained by its outlet pipe in 6 hours. The tank was emptied for repairs. When repairs were done both supply pipes began to fill the tank, but the drain valve was left open by mistake. How long would you expect it to take to fill the tank with the drain shut? How long will it actually take with the drain open?

Still I have trouble with the setup of this type of question

A certain tank can be filled by one supply pipe in 3 hours and by a second supply pipe in 4 hours. The tank can be drained by its outlet pipe in 6 hours. The tank was emptied for repairs. When repairs were done both supply pipes began to fill the tank, but the drain valve was left open by mistake. How long would you expect it to take to fill the tank with the drain shut? How long will it actually take with the drain open?

Still I have trouble with the setup of this type of question

I have the answers I just need to know how to get to them ... the first one is 1.7 hours if the drain was shut and the second is 2.4 hours if the drain is open. I usually use x as some value but in this case I am not sure of how to set it up

I was not able to go very far. I have done other problems but this one and the others are throwing me for a loop. Not sure how to put the formula together

(1/3 + 1/4) = x flow in with drain shut ... would make common denominator of 12 for each supply pipe and x would be 12x/12 due to value of 1x ... I think

then I think the above with valve open would be (1/3 + 1/4 - 1/6) = 12x/12 ... maybe

A certain tank can be filled by one supply pipe in 3 hours and by a second supply pipe in 4 hours. The tank can be drained by its outlet pipe in 6 hours. The tank was emptied for repairs. When repairs were done both supply pipes began to fill the tank, but the drain valve was left open by mistake. How long would you expect it to take to fill the tank with the drain shut? How long will it actually take with the drain open?

Still I have trouble with the setup of this type of question

How long would you expect it to take to fill the tank with the drain shut - T[sub:2u83cgme]1[/sub:2u83cgme]

How long would you expect it to take to fill the tank with the drain OPEN - T[sub:2u83cgme]2[/sub:2u83cgme]

Flow rate out of the tank = 1/6 tank/hr

Flow rate into the tank = (1/3 + 1/4 = ) 7/12 tank/hr

So in 1 hr the tank fills up (with out-valve shut) 7/12

The tank fills up in [1/(7/12) = 12/7 = 1 5/7 hrs = ] 1 hr and 43 minutes with the out-valve shut. = T[sub:2u83cgme]1[/sub:2u83cgme][/spoiler:2u83cgme]

With out-valve open - in 1 hour - the tank fills up (7/12 - 1/6 =) 5/12 part.

So, with out-valve open, the tank fills up in [1/(5/12) = 12/5 = 2 2/5] 2 hrs and 24 minutes. = T[sub:2u83cgme]2[/sub:2u83cgme][/spoiler:2u83cgme]