# One window washer working alone can wash the windows of a certain building in 15 hours. His partner can do the job in only 10 hours. To the nearest half-hour, how many hours would they need to do the job working together?

6

Explanation

The first window washer takes 15 hours to do the job, so in one hour he does $$\frac {1}{15}$$of the job. The second window washer takes 10 hours to do the job, so in one hour he does$$\frac {1}{10}$$ of the job. Let x be the number of hours they need to finish the job if they do it together. In x hours, the first does$$\frac {1}{15}x$$ of the job and the second does $$\frac {1}{10}x$$ of the job. Together, these fractions should add up to 1 (the whole job).
$$\frac {1}{10}x \times \frac {1}{15}x = 1$$

$$\frac {2}{30}x \times \frac {3}{30}x = 1$$

$$\frac {5}{30}x = 1$$
$$x= 1 \times \frac {30}{5}$$
You could also think: In one hour they do $$\frac {1}{15}$$  ; $$\frac {1}{10}$$ or $$\frac {1}{6}$$of the job, so it would take them 6 hours to do$$\frac {6}{6}$$, or the whole job.