Sumi can wash windows of an office building in 3/4 the time it takes her
apprentice. One day they worked on the building together for 2h 16 min then Sumi
continued alone. It took 4 h 32 min more to complete the job. How long would it
take her apprentice to wash all the windows?
How do you figure it out and what is the answer?
Let x hours represent the solution, how long it would take the apprentice to
wash all the windows
So the apprentice's window-washing rate is 1 set of windows per x hours.
That is to say that the apprentice's window-washing rate is or
Sumi can wash windows of an office building in 3/4 the time it takes her apprentice.
Then Sumi's window-washing rate is 1 set of windows per hours.
Therefore Sumi's window-washing rate is or
We simplify by multiplying top and bottom by 4 getting
. So Sumi's window-washing rate is
One day they worked on the building together...
So their combined rate was the sum of those rates
We simplify
So their combined rate was:
One day they worked on the building together for 2h 16 min
We convert that to an improper fraction of hours.
Since rate×time = production, during that time the fraction of
the set of windows they washed working together was
then Sumi continued alone. It took 4 h 32 min more to complete the job.
We convert that to an improper fraction of hours.
Again, since rate×time = production, during that time the fraction of
the set of windows that Sumi washed working alone was
The equation comes from
Multiply through by 45x
That's 11 hours 20 minutes, so that's how long it would take
the apprentice working alone to wash all the windows.
Edwin