Frustrated with word problem. Please help!

[AZHoldcraft]

Ok, so I'm studying for my Teacher Certification Exam and I have a story problem that I'm losing my mind trying to figure out. The problem is below:

Larry, Moe, and Curly can paint an elephant in 3 minutes. Working alone, Larry can paint the elephant in 10 minutes or Moe can paint the elephant in 6 minutes. How long would it take Curly if he were working alone?

Any help possible would be greatly appreciated!

Thank you!

 

[mmm4444bot]

We call these "work problems". We solve them by looking at the fractional part of the job completed per unit of time for each participant.

In this exercise, the time unit is minutes.

Now, we write expressions for the fractional part of the job completed per minute by each stooge.

It takes Larry 10 minutes to do the job; therefore, Larry completes 1/10th of the job per minute.

Likewise, Moe completes 1/6th of the job per minute.

Let x represent the unknown number of minutes that it takes Curly to complete the entire job alone.

Then, Curly completes 1/xth of the job per minute.

The three fractional amounts must add up to the fractional part of the job completed per minute, with all stooges working together.

1/10 + 1/6 + 1/x = 1/3

Solve for x, and you will know how many minutes it takes Curly when working alone.

MY EDIT: Fixed pho paw, then came back and clarified some wording.

 

[AZHoldcraft]

Re:

We call these "work problems". We solve them by looking at the fractional part of the job completed per unit of time for each participant.

In this exercise, the time unit is minutes.

Now, we write expressions for the fractional part of the job completed per minute by each stooge.

It takes Larry 10 minutes to do the job; therefore, Larry completes 1/10th of the job per minute.

Likewise, Moe completes 1/6th of the job per minute.

Let x represent the unknown number of minutes that it takes Curly to complete the entire job alone.

Then, Curly completes 1/xth of the job per minute.

The three fractional amounts must add up to the whole job, with stooges working together.

1/10 + 1/6 + 1/x = 1

Solve for x, and you will know how many minutes it takes Curly when working alone.

Thanks, that's how I had originally set it up, but it doesn't work out to the answer I'm given at the back of the book. The answer is that it takes Curly 15 minutes.

Given the answer, the problem as you setup would be 1/10 + 1/6 + 1/15 = 1. With the LCD being 30, multiplying both sides by 30 would result in:

3 + 5 + 2 = 30, which obviously isn't true.

Should I set up this problem, the way you stated earlier, but instead of setting it equal to 1, setting it 1/3 since it takes the three of them 3 minutes to complete it and since we're putting the time in the denominator?

That would give us:

1/10 +1/6 +1/x = 1/3
3x +5x +30 = 10x
8x + 30 = 10x
2x = 30
x = 15

Does this make sense? Talking through it here has helped me see the answer, but I want to make sure I understand why i set it up that way.

Thanks again.

 

[mmm4444bot]

I missed an error, while proofreading my first post. (Fixed now.) Please excuse me.

Yes, you are correct. The whole job takes 3 minutes when they work together, so the fractional part of the job completed by all per minute is 1/3rd of a washed elephant.

15 minutes is the correct answer. Your book is wrong, if it states a different answer.

These exercises are all about thinking in terms of fractional parts of some total task (work) completed per unit of time, whether working alone or with others.

Cheers !

 

[AZHoldcraft]

Great thank you! After going through and looking at it from your first post I was able to get a better understanding and derive how to get the answer. This should help a lot!

 

[Denis]

Re:

I missed an error, while proofreading my first post. (Fixed now.) Please excuse me.

Go join Subhotosh standing in the corner !

 

[BigGlenntheHeavy]

\(\displaystyle Rate \ of \ each \ Individual \ X \ their \ Time \ = \ Fractional \ Part \ of \ Work \ Done \ (Work \ formula).\)

\(\displaystyle Larry: \ \frac{1}{10} \ \ \ \ \ X \ \ \ 3 \ \ \ \ = \ \frac{3}{10}.\)

\(\displaystyle Curly: \ \frac{1}{6} \ \ \ \ \ \ X \ \ \ 3 \ \ \ \ = \ \frac{1}{2}.\)

\(\displaystyle Moe: \ \frac{1}{x} \ \ \ \ \ \ X \ \ \ 3 \ \ \ \ = \ \frac{3}{x}.\)

\(\displaystyle Hence \ \frac{3}{10}+\frac{1}{2}+\frac{3}{x} \ = \ 1 \ (unity, \ the \ complete \ job).\)

\(\displaystyle Moe's \ rate \ = \ \frac{1}{15} \ or \ it \ takes \ him \ 15 \ min. \ working \ alone \ to \ paint \ the \ elephant.\)

\(\displaystyle Note: \ Knowing \ the \ formula \ (see \ first \ line) \ for \ work \ problems \ usually \ makes \ them \ a \ breeze.\)

\(\displaystyle And \ don't \ forget, \ according \ to \ Charles \ Dickens; \ "Most \ people \ are \ willing \ to \ work \ and \ the\)

\(\displaystyle rest \ are \ willing \ to \ let \ them".\)

\(\displaystyle Oh, \ and \ while \ I'm \ at \ it, \ another \ quote, \ this \ one \ from \ Groucho \ Marx \ concerning \ elephants,\)

\(\displaystyle "Last \ night \ I \ shot \ an \ elephant \ in \ my \ pajamas. \ How \ he \ got \ into \ my \ pajamas, \ I'll \ never \ know."\)