Do two distinct lines always intersect at a point.
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L = hours for the slower pump to fill the pool
L - 5 = hours for the high power pump, since it can do it in 5 hours less.
since the slower pump takes L hours, the faster pump takes then L - 5 hours.
we know both pumps together take 3 hours to do <u>half of the pool</u>, so that means that to fill up <u>the whole pool it takes them 6 hours</u>.
since the slower pump can do it alone in L hours, in 1 hour it has done 1/L of the whole thing.
likewise, since the faster pump can do it in L-5 hours, in 1 hour alone it has done 1/(L-5) of the whole job.
now, we can't use L = 2, because, the whole job by both is done in 6 hours, there's no way the slower pump can do it in less than that, so L = 15.
now if L = 15, then L - 5 = 10.