Question 112134
Let x=the time it takes both pumps working together to fill the tank after the second pump is opened.
Now the first pump can fill at the rate of 1/25 tank per minute
The second pump can fill at the rate of 1/50 tank per min
Together they can fill at the rate of 1/50+1/25 =1/50+2/50=3/50 tank per minute

If we open the first pump for 5 min, then it fills (1/25)*5 or 1/5 of the tank leaving 4/5 of the tank to be filled by pump #1 and #2 working together

So our equation to solve is:

(3/50)x=4/5  multiply each term by 50
3x=40  divide both sides by 3

x=13.333333333 minutes ---------time to fill the tank after pump #2 is opened

Total time, of course, would be 13.333333333333+5 or 18.33333333333 min

CK
(3/50)(13.333333333)+(2/50)(5)=1   (one tank, that is)
40/50+10/50=1
1=1

Hope this helps---ptaylor