word problem: A tank can be filled in 6 hours and drained in

[RossK]

Ok. I have some math homework. I would like to know what I need to read up on to know how to solve the problems. Also I can do the equations to solve them; I can't figure out how to turn the written problems into equations. Here is one of the problems:

A tank can be filled in 6 hours and drained in 18 hours. If the drain is left open, how many hours will it take them to fill the tank?

What I did was the following:

. . .(x/6) + (x/18) = 1
. . .108(x/6) + 108(x/18) = 108(1)
. . .18x + 6x = 108 = 24x
. . .x = 4.5

Which I know can't be the answer.

Thanks for any and all help.

 

[skeeter]

rate the tank can be filled = (1 tank)/(6 hrs)
rate the tank can be drained = (1 tank)/(18 hrs)

[(1 tank)/(6 hrs) - (1 tank)/(18 hrs)](t hrs) = 1 tank filled

t/6 - t/18 = 1

solve for t

 

[RossK]

t = 9.

Thanks for the answer. I hope I will be able to do the rest of the problems now

 

[Denis]

Can be done this simple way:
1 hour = 1/6 - 1/18 = 1/9 : 1/9 * 9 = 1; so 9 hours