Question

Two taps together can fill a tank completely in `(3)1/13` minutes. The smaller tap takes 3 minutes more than the bigger tap to fill the tank. How much time does each tap take to fill the tank completely?

Answer 1

Time = `3 1/3 = 40/13` mins

Let the time taken by larger tap be x

∴ The time taken by smaller tap will be x + 3 

According to the given condition,

`1/x + 1/(x + 3) = 1/(40/13)`

`(x + 3 + x)/(x(x + 3)) = 13/40`

`(2x + 3)/(x^2 + 3x) = 13/40`

`(2x + 3)/(x^2 + 3x) = 13/40` .....(By alternendo)

13(x² + 3x) = 40(2x + 3)

13x² + 39x = 80x + 120

13x² + 39x – 80x – 120 = 0

13x² – 41x – 120 = 0

13x² – 65x + 24x – 120 = 0

13x(x – 5) + 24(x – 5) = 0

(13x + 24) (x – 5) = 0

13x + 24 = 0 or x – 5 = 0 

x = `(-24)/13` or x = 5 

Time is natural number

∴ A larger tap takes 5 min.

And smaller tap takes = x + 3 = 5 + 3 = 8 min.