General Mathematics
-you have been partnered with samantha for pouring concrete. It take you 3 hours longer than samantha to pour the driveway pad. Working together, you can complete the job in 2 hours. How long would it take each of you if you did not work together

[tex] samantha\: = x \\ you = x + 3 \\ together = 2 \\ \\ \frac{1}{x} + \frac{1}{x + 3} = \frac{1}{2} \\ \frac{x + 3 + x}{x(x + 3)} = \frac{1}{2} \\ \frac{2x + 3}{x(x + 3)} = \frac{1}{2} \\ 2(2x + 3) = x(x + 3) \\ 4x + 6 = {x}^{2} + 3x \\ {x}^{2} - x - 6 = 0 \\ (x - 3)(x + 2) = 0 \\ x = 3 \: \: \: \: \: \: \: x = - 2 \\ samantha\: = x = 3hours \\ you = x + 3 = 3 + 3 = 6hours[/tex]