#### pleasehelpmethankyou

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Thank you so much!

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- Thread starter pleasehelpmethankyou
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Thank you so much!

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I don't see this as requiring factoring (primarily). Please show us what you have tried, or at least what topics you have recently learned, so we can see where you need help and what sort of help will be useful to you. Did you not read this?

Thank you so much!

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...

www.freemathhelp.com

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Hello! Sorry I didn't see that part in the guidelines. I think I was also trying to say fractions instead of factoring.I don't see this as requiring factoring (primarily). Please show us what you have tried, or at least what topics you have recently learned, so we can see where you need help and what sort of help will be useful to you. Did you not read this?

## Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...www.freemathhelp.com

This is how I tried to solve it:

Since Jacques takes 3/4 hours to fill one shelf, for 15 shelves, it would take (3/4 hours) x (15 shelves) = 11.25 hours

Then, Henri takes 2/3 of Jacques time, so it would take (11.25 hours) x (2/3) = 7.5 hours

I then did 11.25 - 7.5 = 3.75 hours

Recently, I've been learning about basic calculations with fractions like adding and subtracting, multiplying and dividing. I have a bit of difficulty with word problems though, so I would appreciate the help. Thank you.

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Thanks. You did that part well, up to the subtraction at the end.Hello! Sorry I didn't see that part in the guidelines. I think I was also trying to say fractions instead of factoring.

This is how I tried to solve it:

Since Jacques takes 3/4 hours to fill one shelf, for 15 shelves, it would take (3/4 hours) x (15 shelves) = 11.25 hours

Then, Henri takes 2/3 of Jacques time, so it would take (11.25 hours) x (2/3) = 7.5 hours

I then did 11.25 - 7.5 = 3.75 hours

Recently, I've been learning about basic calculations with fractions like adding and subtracting, multiplying and dividing. I have a bit of difficulty with word problems though, so I would appreciate the help. Thank you.

My next question is, have you seen any "time to do a job" problems before, perhaps without fractions? This is commonly taught as part of algebra, but doesn't require it.

The basic idea is that this is really a

Does any of that sound familiar? Try doing whatever you can with this idea.

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For example, if it takes me 15 minutes to complete a task, then I complete 1/15th of the job per minute. (1/15 is the reciprocal of 15.) If it takes you 10 minutes to complete the same task, then you complete 1/10th of the job per minute. (1/10 is the reciprocal of 10.) We add the reciprocals, to find the fractional amount of the task completed per time unit when we work together.

1/15 + 1/10 = 1/6

In other words, working together, we complete 1/6th of the task per minute. We consider the number 1 to represent 100% of the task. Therefore, 1/6th of the job done per minute means that it takes us 6 minutes, working together. (6 times 1/6 equals 1.)

Go through some worked examples, at the link above. See if that helps. Post your attempt, if you'd like more help.

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Ok that makes a lot more sense. I tried starting all over like this:Thanks. You did that part well, up to the subtraction at the end.

My next question is, have you seen any "time to do a job" problems before, perhaps without fractions? This is commonly taught as part of algebra, but doesn't require it.

The basic idea is that this is really arateproblem. You need to find the rate (in shelves per hour, or perhaps supermarkets per hour) for each person, and then add them, because, for example, if I can do something at a rate of 2 tasks per hour, and you can do it at 3 tasks per hour, then together (if we don't interact to help or hinder one another), together we will do 5 tasks per hour.

Does any of that sound familiar? Try doing whatever you can with this idea

For Jacques, it would be 1 shelf per 3/4 hours, so (1)/(3/4) = 1.33 shelves/hour

For Henri, 1 shelf per 1/2 hours, so (1)/(1/2) = 2 shelves/hour

So 1.33 + 2 = 3.33 shelves/hour altogether.

Finally, for 15 shelves it would be 15/3.33 = 4.5 hours?

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Thank you! I'll take a look at the examples later as well.Hello PHMTY. We use reciprocals, when dealing with 'combined work rates' type problems. Seethis page, for some worked examples.

For example, if it takes me 15 minutes to complete a task, then I complete 1/15th of the job per minute. (1/15 is the reciprocal of 15.) If it takes you 10 minutes to complete the same task, then you complete 1/10th of the job per minute. (1/10 is the reciprocal of 10.) We add the reciprocals, to find the fractional amount of the task completed per time unit when we work together.

1/15 + 1/10 = 1/6

In other words, working together, we complete 1/6th of the task per minute. That means it takes us 6 minutes, working together. (6 is the reciprocal of 1/6.)

Go through some worked examples, at the link above. See if that helps. Post your attempt, if you'd like more help.

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ohh ok thanks I'll keep that in mind

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4.5 hours is a correct answer. You method is okay. But, if you're expected to use exact arithmetic (instead of calculator approximations), there might be an issue with your work on a class assignment.(1)/(3/4) = 1.33

15/3.33 = 4.5 hours?

1/(3/4) is not 1.33 (it's actually 4/3).

1.33 is only a decimal

1.33 is exactly 133/100.

Likewise, 15/3.33 is not 4.5

15/3.33 is actually 500/111.

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ah so for the calculations, instead of changing them to decimal form, I would keep the fractions and go like this4.5 hours is the correct answer. You method is okay. But, if you're expected to use exact arithmetic (instead of calculator approximations), there might be an issue with your work on a class assignment.

1/(3/4) is not 1.33 (it's actually 4/3).

1.33 is a decimal approximation for 4/3.

15/3.33 is not 4.5 (it's actually 45/4).

4/3 + 2 = 10/3 shelves per hour

then for 15 shelves: (15) / (10/3) =

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Mr. J fills a shelf in 3/4 hour.

15 × 3/4 = 45/4

Mr. J completes the job in 45/4 hour.

Mr. H requires 2/3 the time Mr. J does, to complete the job.

2/3 × 45/4 = 15/2

Therefore, Mr. J completes 4/45ths of the job per hour, and Mr. H completes 2/15ths of the job per hour. We combine those reciprocals.

4/45 + 2/15 = 2/9

Working together, they complete 2/9ths of the job per hour, so it takes them 9/2 hour to finish.

9/2 = 4.5

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haha ok got it! thank you so much it took me so long to figure this out

Mr. J fills a shelf in 3/4 hour.

15 × 3/4 = 45/4

Mr. J completes the job in 45/4 hour.

Mr. H requires 2/3 the time Mr. J does, to complete the job.

2/3 × 45/4 = 15/2

Therefore, Mr. J completes 4/45ths of the job per hour, and Mr. H completes 2/15ths of the job per hour. We combine those reciprocals.

4/45 + 2/15 = 2/9

Working together, they complete 2/9ths of the job per hour, so it takes them 9/2 hour to finish.

9/2 = 4.5

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Hard earned gains are not easily forgotten. Basic principle of no pain no gain mantra. One has a tendency to remember and value them permanently.haha ok got it! thank you so much it took me so long to figure this out

Last edited:

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2/3 of 3/4 is, of course, 2/4= 1/2 hour. Jacques, filling one shelf in 3/4 hour is working at a rate of 4/3 shelves per hour. Henri, filling one shelf in 1/2 hour, is workingt at a rate of 2 shelves per hour. When people work together, their rates add. So Jacques and Henri, working together fill 4/3+ 2= 4/3+ 6/3= 10/3 shelves per hour.

Thank you so much!

Together they can fill 15 shelves in 15/(10/3)= 15(3/10)= 9/2 or 4 and a half hours.

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i tried to solve it using another way and i'm bringin' it before you to approve of it or destroy it.

I did exactly what the poster did until i found how much hours each of them work.

Jason 3/4 * 15 =45/4=11.25 hrs

Henry 2/3 * 11.25 = 7.5 hrs

here i veered direction and went this way, (though might be the wrong way!)

i set up this formula to find out combined rate of work

t/A + t/B =1

where t = the amount of time working together to accomplish the task

i let Jason be A

I let Henry be B

So, again, here's the formula

t/A + t/B =1

i'll plug in what i have

t/11.25 + t/7.5 =1

i will round up and down to make finding a common denominator easier

t/11 + t/8 =1

common denominator of 8 and 11 =88

___ + _____

88 88

now i will have to multiply both fractions for a number that yields 88.

t/11 (8/8)= 8t/88

t/8 (11/11) =11t/88

so now i can add this fractions

8t/88 + 11t/88 = 19t/88

19t/88=1

solvin' for t

88( 19t/88) = 1 * 88

19t=88

19t/19 =88/19

=4.6 which is pretty close to the result he got.

if Jason and Henri work together they will fill the shelves in approximately 4.6 hours.

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No.i'll plug in what i have

t/11.25 + t/7.5 =1

i will round up and down to make finding a common denominator easier

t/11 + t/8 =1

There are several ways to make it easier without rounding.

One is to just multiply both sides of the equation by 11.25*7.5, which is the actual LCM. You get 7.5t + 11.25t = 84.375. Add and divide, and you get t = 84.375/18.75 = 4.5 hours.

Another way is not to use decimals at all; the two times are 11 1/4 = 45/4 and 7 1/2 = 15/2, so the equation is (4/45)t + (2/15)t = 1. The LCD is 45, so we multiply by that and get 4t + 6t = 45, so that 10t = 45 and t = 45/10 = 4.5 again.

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Please check that. What is 7.5 + 11.25?7.5t+ 11.25 t= 84.375

18.5t=84.375

I showed you the correct work, completely. It gives the exact answer, not one you have to round (incorrectly, even!) at the end.t=4.56081081

t=4.5