Linear Algebra Problem Solving

Question

Three water pipes are connected to a tank. Together, the first and second pipes can fill the tank in 20 hours. Together, the first and the third pipes can fill it in 30 hours and together, the second and the third can fill it in 25 hrs. How much time would be required for the three pipes together to fill the tank?

Answer 1

Let 1st need x hours, 2nd need y- hours and 3rd need z hours.

Then we have equations: 1/x + 1/y = 1/20; 1/x + 1/z = 1/30; 1/y + 1/z = 1/25.

If we add all 3 equations we get: 2/x + 2/y + 2/z = 1/20 + 1/30 + 1/25 = (15 + 10 + 12)/300 = 37/300

So, 1/x + 1/y + 1/z = 37/600 = 1/(600/37) and 3 pipes working together can fill tank for 600/37 = 16 and 8/37 hr