The experienced window washer can wash all the windows in Mike’s house in 2 hours, which implies that in 1 hour he completes 1/2 of the job.
By the same logic, the new trainee completes 1/7 of the job in one hour.
If they work together, they complete
[tex]\dfrac{1}{2}+\dfrac{1}{7}=\dfrac{7}{14}+\dfrac{2}{14}=\dfrac{9}{14}[/tex]
of the job in one hour, meaning that they complete the job in 14/9 of a hour.
Answer:
It would take 1.55 hours or 93.6 minutes for them if they work together.
Solution:
Let us assume together both can complete the work in x hours.
Experienced window washer can wash the house in 2 hours.
So, in 1 hour he will do, [tex]\frac{1}{2}[/tex] part of the house
Hence, in x hours he will do [tex]\frac{x}{2}[/tex] part of the house
Again the trainee can wash all the windows in 7 hours
So, in 1 hour he will do, [tex]\frac{1}{7}[/tex] part of the house
Hence, in x hours he will do[tex]\frac{x}{7}[/tex] part of the house
We can now say,
[tex]\Rightarrow \frac{x}{2}+\frac{x}{7}=1[/tex]
[tex]\Rightarrow \quad x \times\left(\frac{7+2}{14}\right)=1 \\\\ \Rightarrow x \times\left(\frac{9}{14}\right)=1 \\\\ \Rightarrow x=\frac{14}{9}=1.55[/tex]
They can complete in 1.55 hours.
1 hour = 60 minutes
So, according to unitary method, [tex]1.55 hours = 1.55\times60 \Rightarrow 93.6 minutes[/tex].
