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?
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.