Brett usually takes 50 minutes to groom the horses. After working 10 minutes he was joined by Kathy and they finished the grooming in 15 minutes. How long would it have taken Kathy working alone?

$30 \setminus \setminus \textrm{\min u t e s}$

Explanation:

Let $x$ minutes be the time taken alone by Kathy to groom the horses then

Work done by Brett in $10$ minutes

$= \frac{10}{50} = \frac{1}{5}$

The work left after Brett has worked for $10$ minutes

$= 1 - \frac{1}{5} = \frac{4}{5}$

Now, the left work $\frac{4}{5}$ will be done by Kathy & Brett together in $15$ minutes hence we have

$15 \left(\frac{1}{50} + \frac{1}{x}\right) = \frac{4}{5}$

$15 \left(\setminus \frac{50 + x}{50 x}\right) = \frac{4}{5}$

$x = 30$

hence Kathy alone takes $30$ minutes to groom horses