Question

One pipe can fill a rank in3 hour less than another twp pipe together can fill the tank in 6 hour 40 minute fond the time each pipi will rake to fill tank

Answer 1

Let one pipe fills in x hrs. Then, other one fills in x-3 hrs.
Together they fill in
$\frac{x(x - 3)}{x + (x - 3)} = \frac{x(x - 3)}{2x - 3} \: hrs \\ given \: \: \frac{x(x - 3)}{2x - 3} = 6 \: hr \: \: 40 \: min \\ \frac{x(x - 3)}{2x - 3} = 6 + \frac{40}{60} = \frac{20}{3} \\ 3x(x - 3) = 20(2x - 3) \\ 3 {x}^{2} - 49x + 60 = 0 \\ x = \frac{49 + \: or \: - \sqrt{ {49}^{2} - 4 \times 3 \times 60} }{2 \times 3} \\ = \frac{49 + \: or \: - 41}{6} = 15 \: \: or \: \: \frac{4}{3} \\ \\ x = \frac{4}{3} \: \: is \: \: not \: \: possible \: since \\ x - 3 \: \: gives \: \: - ve \: \: value \\ \\ so \: \: x = 15 \: \: hrs$
Thus, one pipe fills in 15 hrs and other pipe fills in 15-3 = 12 hrs