MHB How do I find the fraction of the job done?

[jaytheseer]

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

 

[Deveno]

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.

 

[jaytheseer]

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.

 

[Prove It]

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.

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?

 

[jaytheseer]

Got it! Thanks guys! :)

 

[Prove It]

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...