Question

Two pipes together can fill a water tank in 6 hours and 40 minutes. Find the time each will take to fill the tank if one of the two pipes can fill it in 3 hours less than the other

Answer 1

x and y are time for each tap, i forgot to write 3x60 to convert to mins

Answer 2

Two pipes together can fill a water tank in
6 hours 40 minute=6+40/60= 20/3 hours
according to the question
$\frac{1}{x} + \frac{1}{x - 3} = \frac{1}{ \frac{20}{3} } \\ \frac{1}{x} + \frac{1}{x - 3} = \frac{3}{20} \\ \frac{x - 3 + x}{x (x - 3)} = \frac{3}{20} \\ \frac{2x - 3}{ {x}^{2} - 3x} = \frac{3}{20} \\ 3 {x}^{2} - 9x = 40x - 60 \\ 3 {x}^{2} - 9x - 40x + 60 \\ 3 {x}^{2} - 49x + 60 = 0 \\ 3 {x}^{2} - 45x - 4x + 60 = 0 \\ 3x(x - 15) - 4(x - 15) = 0 \\ (3x - 4)(x - 15) = 0 \\ either \: x - 15 = 0 \\ x = 15 \\ or \: 3x - 4 = 0 \\ 3x = 4 \\ x = \frac{4}{3}$