a tank can be filled by one pipe in 3

Question

.5 hours and emptied by another in 4.2 hours.if both ipes are running, how long will it take to fill an empty tank?

Answer 1

in work problems like this, think of the amount of work each person can do in the unit of time.

if pipe a can fill the tank in 3.5 hours, then in one hour it can fill 1/3.5 of the tank.

The other pipe b can fill 1/4.2 of the tank in one hour.

So, in one hour, both pipes working together can fill up

1/3.5 + 1/4.2 = 0.5238 of the tank

So, to fill the whole tank, it will take 1/.5328 hours, or 1.90909 = 1 10/11 hours

In general, if various workers can do the job in a,b,c,... units of time, then working together they can do it in n units of time:

1/n = 1/a + 1/b + 1/c + ...

Answer 2

I see I misread the problem. It was answered correctly later on