Two pumps of different sizes, working together, can empty a fuel tank in 3 hours. the larger pump can empty the tank in 4 hours less than the smaller one. if the larger pump is not working, how long will it take the smaller pump to do the job alone?

Let's say the larger pump takes "a" hours to empty the whole lot.

and let's say the smaller pump takes "b" hours to empty it by itself.

but we know that if both team up, they get it done in 3 hours flat.

now, if we know the large pump takes "a" hours, how many hours has it done in say 1 hour?  well, it has only done thus far 1/a of the total work.

and we know the small one takes "b" hours, so in 1 hour it has done only thus far 1/b of the whole lot, just that much.

we know, both teaming up can do it in 3 hrs, so in just 1 hr, they have both done only 1/3 of the total work.



but we know that, whatever "b" hours is, we know that the large pump can do it 4 hours less than that, so, it can do it in "b - 4", namely, a = b - 4.





well, it can't be 1.394 because that'd make b - 4 a negative value, so it has to be the other value.