A tank can be filled by one pipe in x minutes and emptied by another p

1.	A tank can be filled by one pipe in x minutes and emptied by another pipe in (x+5)minutes. Both the pipes when opened together can fill the empty tank in 16.8minutes. Find x.(EXEMPLAR PROBLEM)
Answer» In one minute 1/x part of tank is filled by the first pipe only. When both pipes are opened, in one minute part of tank filled is1/x-1/x+5 = 5/x(x+5) The problem tells us that the tank gets filled in 16.8 minutes. In one minute 1/16.8 part is filled. So, 5/x(x+5) = 1/16.8x(x+5)/5 = 16.8x(x+5) = 84 x^2+5x-84 = 0 (x+12)(x-7) = 0 x = -12 or x = 7x = -12 is rejected. The only solution is x = 7

A tank can be filled by one pipe in x minutes and emptied by another pipe in (x+5)minutes. Both the pipes when opened together can fill the empty tank in 16.8minutes. Find x.(EXEMPLAR PROBLEM)

Answer»

In one minute 1/x part of tank is filled by the first pipe only.

When both pipes are opened, in one minute part of tank filled is1/x-1/x+5 = 5/x(x+5)

The problem tells us that the tank gets filled in 16.8 minutes. In one minute 1/16.8 part is filled.

So, 5/x(x+5) = 1/16.8x(x+5)/5 = 16.8x(x+5) = 84 x^2+5x-84 = 0 (x+12)(x-7) = 0 x = -12 or x = 7x = -12 is rejected.

The only solution is x = 7