Time to Fill Up The Tank

There are 2 taps to fill a big tank; one is bigger & other is smaller. A bigger alone can fill up the tank in 5 hours less than smaller tap can alone. Both taps together take 6 hours to fill up the tank.

How many hours required separately for smaller & bigger taps to fill up the tank?

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Hours Needed By Each Tap

What was the question? 

Let x be hours required for bigger tap then smaller needs x + 5
hours.

In 1 hour bigger fills 1/x & smaller fills 1/(x+5) part of the tank. Together both take 6 hours to completely fill the tank. So,

1/x + 1/(x+5) = 1/6

6(x + 5 + x) = x^2 + 5x

x^2 - 7x - 30 = 0

(x-10) (x+3) = 0

x + 3 = 0 gives x = -3 which is not possible as x represents hours.

So x - 10 = 0 gives x = 10.

Hence for a bigger tap 10 hours & for smaller tap 10 + 5 = 15 hours required to fill up the tank!