Two tailors together stitch a batch of school uniforms in 6 days. Working alone, one of them takes 5 days more than the other. How many days would the slower tailor take alone?

Explanation

1. 01

   Let the faster tailor take $x$ days; the slower takes $x + 5$.

2. 02

   $\frac{1}{x} + \frac{1}{x+5} = \frac{1}{6}$, so $6(2x + 5) = x(x + 5)$.

3. 03

   $x^2 - 7x - 30 = 0$, i.e. $(x - 10)(x + 3) = 0$, so $x = 10$.

4. 04

   The slower tailor takes $10 + 5 = 15$ days.