Acistern can be completely drained by a pipe in 6 hours. it can be filled by two pipes in 4 hours and 5 hours, respectively. how many hours will the empty cistern take to fill if all the pipes are running? if x is the time to fill it, which of the following equations could be used to solve for t?
a. 4x + 5x - 6x = 1
b. 15x + 12x - 10x = 60
c. 4x + 5x = 20

Let's say the pipes are "a",  to drain it in 6hours, "b" to fill it up by itself in 4hours and "c" to fill it up in 5 hours.

so..."a" can drain it in 6hours, that means, in 1 hour, "a" has only done 1/6 of the job, because in 6 hours, it would have done 6/6 or 1 whole, the whole job, the cistern fully filled up, but, in 1 hour, it has only done 1/6 of that.

"b" in 1 hour, has only done 1/4 of the whole job then.
"c" in 1 hour has only done 1/5 of the whole job then.

now... let's say it took "x" hours, if we have "a", "b" and "c" running, a draining away whilst b and c filling it up.

since it takes "x" hours to fill the cistern, after 1 hour, all three have only done 1/x of the whole job.

well, let's add their rates, to see what we get then.



how long does it take to fill the cistern? well, just solve for "x".