SOLUTION: 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

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 974568: 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?
Ho w do you figure it out and what is the answer?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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 matrix%281%2C4%2C1%2Cset%2Cof%2Cwindows%29%2Fmatrix%281%2C2%2Cx%2Chours%29 or matrix%281%2C2%2C+1%2Fx%2C+matrix%281%2C3%2Cset%2Cof%2Cwindows%29%2Fhr%29%29

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 expr%283%2F4%29x hours.

Therefore Sumi's window-washing rate is matrix%281%2C4%2C1%2Cset%2Cof%2Cwindows%29%2Fmatrix%281%2C2%2Cexpr%283%2F4%29x%2Chours%29 or matrix%281%2C2%2C+1%2Fexpr%283%2F4%29x%2C+matrix%281%2C3%2Cset%2Cof%2Cwindows%29%2Fhr%29%29

We simplify 1%2Fexpr%283%2F4%29xby multiplying top and bottom by 4 getting
4%2F%283x%29. So Sumi's window-washing rate is

matrix%281%2C2%2C+4%2F%283x%29%2C+matrix%281%2C3%2Cset%2Cof%2Cwindows%29%2Fhr%29%29

One day they worked on the building together...
So their combined rate was the sum of those rates

matrix%281%2C2%2C+1%2Fx%2B4%2F%283x%29%2C+matrix%281%2C3%2Cset%2Cof%2Cwindows%29%2Fhr%29%29

We simplify 1%2Fx%2B4%2F%283x%29=3%2F%283x%29%2B4%2F%283x%29=7%2F%283x%29

So their combined rate was:

matrix%281%2C2%2C+7%2F%283x%29%2C+matrix%281%2C3%2Cset%2Cof%2Cwindows%29%2Fhr%29%29

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

%287%2F%283x%29%29%2A%2834%2F15%29%22%22=%22%22matrix%281%2C6%2C238%2F%2845x%29%2Cof%2Cthe%2Cset%2Cof%2Cwindows%29

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

%284%2F%283x%29%29%2A%2868%2F15%29%22%22=%22%22matrix%281%2C6%2C272%2F%2845x%29%2Cof%2Cthe%2Cset%2Cof%2Cwindows%29

The equation comes from

%22%22%2B%22%22%22%22=%22%22%28matrix%285%2C1%2C%0D%0A%0D%0A1%2Ccomplete%2Cset%2Cof%2C+windows%29%29



Multiply through by 45x

238%2B272%22%22=%22%2245x

510%22%22=%22%2245x

510%2F45%22%22=%22%22x

34%2F3%22%22=%22%22x

11%261%2F3%22%22=%22%22x

That's 11 hours 20 minutes, so that's how long it would take
the apprentice working alone to wash all the windows.

Edwin