how many days will take

eddy2017

eddy2017

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Joined
Oct 27, 2017
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Hi, dear tutors, this problem is not giving me the chosen answer when i work it out.

A carpenter can make 3 cabinets in two days. how many days will take an apprentice working half as fast to make 9 cabinets.

i am setting this up as a proportion
cabinets --------------time
3-----------------------2 days
9-----------------------x

3x= 9*2
3x=18

3x/3 = 18/3

x=6
It should take the apprentice 6 days
but in the answer choice the answer which is given as the right answer says 12.
am I missing something here?
thanks,
eddy
 
eddy2017 said:
Hi, dear tutors, this problem is not giving me the chosen answer when i work it out.

A carpenter can make 3 cabinets in two days. how many days will take an apprentice working half as fast to make 9 cabinets.

i am setting this up as a proportion
cabinets --------------time
3-----------------------2 days
9-----------------------x

3x= 9*2
3x=18

3x/3 = 18/3

x=6
It should take the apprentice 6 days
but in the answer choice the answer which is given as the right answer says 12.
am I missing something here?
thanks,
eddy






​

Click to expand...
The carpenter is working half as fast, i.e. taking him twice as long.
 
eddy2017 said:
Hi, dear tutors, this problem is not giving me the chosen answer when i work it out.

A carpenter can make 3 cabinets in two days. how many days will take an apprentice working half as fast to make 9 cabinets.

i am setting this up as a proportion
cabinets --------------time
3-----------------------2 days
9-----------------------x

3x= 9*2
3x=18
3x/3 = 18/3
x=6
It should take the apprentice 6 days
but in the answer choice the answer which is given as the right answer says 12.
am I missing something here?
thanks,
eddy

​

Click to expand...
To solve this problem, I would ask & answer following questions:

How many days the Carpenter take to make 1 cabinet = 2/3 days

At half efficiency, how many days would the apprentice take to make 1 cabinet = 2
* 2/3 days

How many days would the apprentice take to make 9 cabinets = 9 * 2 * 2/3 days
 
Subhotosh Khan said:
To solve this problem, I would ask & answer following questions:

How many days the Carpenter take to make 1 cabinet = 2/3 days

At half efficiency, how many days would the apprentice take to make 1 cabinet = 2
* 2/3 days

How many days would the apprentice take to make 9 cabinets = 9 * 2 * 2/3 days
Click to expand...
but I'm not getting something.
________
At half efficiency, how many days would the apprentice take to make 1 cabinet = 2
* 2/3 days

Why 2?. Where is this 2 coming from?
 
How many days the Carpenter take to make 1 cabinet = 2/3 days

I suppose the 2/3 comes from 2 cabinets in 3 days, right?
 
eddy2017 said:
but I'm not getting something.
________
At half efficiency, how many days would the apprentice take to make 1 cabinet = 2
* 2/3 days

Why 2?. Where is this 2 coming from?
Click to expand...
When the efficiency is halved (1/2)
The time is doubled (1/(1/2) =2)
 
Subhotosh Khan said:
To solve this problem, I would ask & answer following questions:

How many days the Carpenter take to make 1 cabinet = 2/3 days

At half efficiency, how many days would the apprentice take to make 1 cabinet = 2
* 2/3 days

How many days would the apprentice take to make 9 cabinets = 9 * 2 * 2/3 days
Click to expand...
9 × 2× 2/3
18 × 2/3
Reducing it
6× 2= 12
Thanks. I got it.
 
Subhotosh Khan said:
When the efficiency is halved (1/2)
The time is doubled (1/(1/2) =2)
Click to expand...
I see this now. Just one question.
When efficiency is halved, will I always have to multiply the 1/2 by 1 to get 2 ?.
I mean, is this a set operation?
 
eddy2017 said:
I see this now. Just one question.
When efficiency is halved, will I always have to multiply the 1/2 by 1 to get 2 ?.
I mean, is this a set operation?
Click to expand...
Eddy

Algebra is about generalization. Trying to make rules from a single numerical example is not efficient.

What is the rate at which the carpenter makes a cabinet? This will be a ratio between cabinets and time.

[math]\text {Carpenter's rate} = \dfrac{\# \text { of cabinets}}{\# \text { of days}}.[/math]
When you see the word "rate," ask yourself whether time will be in the denominator.

Where the ratio comes in is in the concept of comparative efficiency. Notice that word "comparative." What does it mean in the context of this problem. It means

[math]\dfrac{\text {apprentice's rate}}{\text {carpenter's rate}} = \dfrac{1}{2} \implies \\ 2 * \text {apprentice's rate} = \text {carpenter's rate} \implies\\ \text {apprentice's rate} = \dfrac{1}{2} * \text {carpenter's rate.}[/math]
If what you put in your head is one-half, when you get a problem with a different ratio of efficiency, the one half will do you not a lick of good. You need to understand the logic of the process so you can apply it in different circumstances. Make sense?
 
Last edited:
JeffM said:
Eddy

Algebra is about generalization. Trying to make rules from a single numerical example is not efficient.

What is the rate at which the carpenter makes a cabinet? This will be a ratio between cabinets and time.

[math]\text {Carpenter's rate} = \dfrac{\# \text { of cabinets}}{\# \text { of days}}.[/math]
When you see the word "rate," ask yourself whether time will be in the denominator.

Where the ratio comes in is in the concept of comparative efficiency. Notice that word "comparative." What does it mean in the context of this problem. It means

[math]\dfrac{\text {apprentice's rate}}{\text {carpenter's rate}} = \dfrac{1}{2} \implies \\ 2 * \text {apprentice's rate} = \text {carpenter's rate} \implies\\ \text {apprentice's rate} = \dfrac{1}{2} * \text {carpenter's rate.}[/math]
If what you put in your head is one-half, when you get a problem with a different ratio of efficiency, the one half will do you not a lick of good. You need to understand the logic of the process so you can apply it in different circumstances. Make sense?
Click to expand...
It makes a world of sense now. Thank you, Jeff. Good to hear from you. Best regards.
 
eddy2017 said:
always have to multiply the 1/2 by 1 to get 2 ?
Click to expand...
That statement/question does not make sense. Please rephrase it.

Another thing - "always" is very very long time.

In science, we avoid using that adverb - always :ROFLMAO::ROFLMAO::ROFLMAO::ROFLMAO:
 
You said: *
When the efficiency is halved (1/2)
The time is doubled (1/(1/2) =2)

I thought it was a constant.
Jeff cleared it up for me.
 
A constant is an 'always'. How bout that?. The joke is on you now ? ?
 
Subhotosh Khan said:
From where did you get "multiply"?
Click to expand...
No, my error. I saw the divison bar now.
Why do you divide 1/ 1/2 . I know that equals 2
Why the division though?
I guess 1 represents the rate speed of the carpenter here divided by the apprentice 's rate of speed. He works at half the speed, is this okay?.
 
They might be spelled differently but the idea is the same. A constant or konstant never change. Pi will always be Pi, I guess.
 
eddy2017 said:
They might be spelled differently but the idea is the same. A constant or constant never change. Pi will always be Pi, I guess.
Click to expand...
No - gravitational constant changes over time - then you shall have no 'pie'!!!

π is 3.14159..... whatever the number is only in western thoughts. In eastern classical definition - that "constant" is expressed as (C/D).

See even Pi is not constant - eat it.....
 
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