Tank Q4

[jwednesday]

another word problem

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

 

[Deleted member 4993]

another word problem

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

Start naming things to find.

How long would you expect it to take to fill the tank with the drain shut - T[sub:1drprk9i]1[/sub:1drprk9i]

How long would you expect it to take to fill the tank with the drain OPEN - T[sub:1drprk9i]2[/sub:1drprk9i]


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

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

Now what....

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[jwednesday]

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

 

[Deleted member 4993]

How far did you go with the hints I have provided?

In these types of problems, 90% of the work is set-up. Other 10% is grunt work to get the numbers with calculators.

 

[jwednesday]

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

 

[jwednesday]

wait ... the light bulb just went on. I understand what you are telling me now. ... just not sure where the variable x would go

 

[jwednesday]

(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

 

[Deleted member 4993]

another word problem

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

Start naming things to find.

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

Spoiler: :2u83cgme

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.

Spoiler: :2u83cgme

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]

 

[jwednesday]

the answer is:

valve closed

x/3 + x/4 = 1 .. 4x/12 + 3x/12 = 12/12 .. 4x + 3x = 12 .. 7x = 12 .. 7x/7 = 12/7 .. x = 1.7 hours

valve open

x/3 + x/4 - x/6 = 1 .. 4x/12 + 3x/12 - 2x/12 = 12/12 .. 7x-2x = 12 .. 5x = 12 .. 5x/5 = 12/5 .. x= 2.4