Question

P and Q completed a job working together in x days
P takes (X + 8) days to complete the job; Q takes
(x + 18) days to complete the job. Find x.​

Answer 1

Answer:

12

Step-by-step explanation:

P alone can do the work in (X + 8) days

Q alone can do the work in (X + 18) days

Both working together can do the work in (X) days

By given information and using the inverse method

$\frac{1}{x + 8} + \frac{1}{x + 18} = \frac{1}{x} \\ \\ \frac{x + 18 + x + 8}{ {x}^{2} + 18x + 8x + 144 } = \frac{1}{x} \\ \\ x(2x + 26) = {x}^{2} + 26x + 144 \\ \\ 2 {x}^{2} + 26x = {x}^{2} + 26x + 144 \\ \\ {x}^{2} = 144 \\ \\ x = 12$