How do I find the fraction of the job done?

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SUMMARY

In the discussion, participants analyze how much of a job can be completed in a given timeframe, specifically calculating the fraction of windows washed by a worker in 6 days when the total job takes 9 days. The correct answer is determined to be 2/3 of the windows. The solution involves setting up a ratio of the work done to the time taken, simplifying the calculation by dividing the total work by the number of days, and then multiplying by the number of days worked.

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If a worker can wash all the glass windows of a building in 9 days, what part of the job can
said workers finish in 6 days?1. ¼
2. 1/3
3. 2/3
4. 3/5
5. ¾
 
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Re: Need EXPLANATION on how to solve this one. Thanks!

Here is a hint: If it takes 9 days to wash ALL the windows, what fraction of the total will the worker wash in ONE day? (What number is 1 part of 9 making a whole)?

Multiply your answer to THAT question by six. You may have to "reduce" your final answer.
 
Re: Need EXPLANATION on how to solve this one. Thanks!

Is it 2/3? I tried to draw a figure to be able to visualize it (and it takes much time). I don't know other ways to solve it. :confused:
 
Re: Need EXPLANATION on how to solve this one. Thanks!

jaytheseer said:
Is it 2/3? I tried to draw a figure to be able to visualize it (and it takes much time). I don't know other ways to solve it. :confused:

No drawings are needed. But your answer is correct, in 6 days one person can wash 2/3 of the windows. The easier way is to use ratios.

Set up a ratio "Proportion of the windows washed : Number of days", in this case it will be 1:9. So if you wanted to know how much in one day, you simply have to divide both sides by 9, giving 1/9 : 1 (in other words, 1/9 of the windows in 1 day), then for six days multiply everything by 6, giving 6/9 : 6, or if you like, 2/3 : 6 (2/3 of all the windows will be done in 6 days).

Can you go from here?
 
Got it! Thanks guys! :)
 
Having said that no drawings were necessary, I'd still be very interested in seeing them, as I love seeing different ways to solve problems and will never discourage a student's creativity...
 

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