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?



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.

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