Question

two water taps together can fill a tank in 2 11/12 hrs (mixed fration ). the tap of smaller diameter takes 2hrs more than the larger one to fill the tank seperately .find the time in which each tap can separately fill the tank? plss explain with steps

Answer 1

Let the time taken by larger tap be x hrs
Then, time taken by smaller tap is x+2 hrs
They together take
$\frac{x(x + 2)}{x + (x + 2)} \: hrs \: \: to \: \: fill$
Given,
$\frac{x(x + 2)}{x + (x + 2)} = 2 \frac{11}{12} = \frac{35}{12} \\ 12x(x + 2) = 35(2x + 2) \\ 6x(x + 2) = 35(x + 1) \\ 6 {x}^{2} - 23x - 35 = 0 \\ x = \frac{23 + \: or \: - \sqrt{ {23}^{2} - 4 \times 6 \times - 35} }{2 \times 6} \\ x = \frac{23 + \: or \: - 37}{12} \\ taking \: \: positive \: \: value \\ x = \frac{23 + 37}{12} = 5$
Thus time taken by larger tap is 5 hrs and by smaller tap is 5+2 = 7 hrs