Word problem dealing with rate. Solve for rate of variable.

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Homework Help Overview

The problem involves determining the rate at which two employees produce widgets, given that one employee takes twice as long as the other. The scenario describes a collaborative effort where both employees together produce a total of 15 widgets in a day.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the rates of the two employees, with some attempting to express the rate of employee A in terms of employee B. Questions arise regarding the correct interpretation of the time taken by each employee and how it affects their production rates.

Discussion Status

There is an ongoing exploration of the relationships between the rates of the employees, with some participants clarifying their understanding of how the time taken by each employee influences the number of widgets produced. Multiple interpretations of the problem are being considered, and some participants express realization of earlier misunderstandings.

Contextual Notes

Participants are navigating the constraints of the problem, specifically the implications of one employee taking twice as long as the other, which affects their respective production rates. There is an acknowledgment of the need to clarify definitions and relationships between the variables involved.

aifan
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Homework Statement



You run a small business making widgets. You have two employees. Employee A takes two times as long as employee B to make a widget. During each day, both employees working together will make 15 widgets, how many widgets get made by employee A each day?

Homework Equations



rate = area/time

The Attempt at a Solution


I know the answer is 5 but I don't understand why. Here is my attempt.

A = 2*B<--- A takes twice the time of B
B = B

since I am suppose to be solving for A write in terms of A
B = A/2

so their rate together should be A + B = 15 widgets.

A/2 + A/2 = 15and this is were I get stuck.
 
Last edited:
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aifan said:
...their rate together should be A + B = 15 widgets.

What is A equal to?
 
A is equal to 2B.
I tries doing 2B + B = 15
which is 5 but that is solving for B not A
 
Well you know what A + B equals to. So A = ?
 
A = 15 - b
 
I guess we need A=1/2B (or B=2A) since were talking about how many widgets A can make compared to B.

Sorry about that.
 
But A takes longer than B it takes twice as long as B does so A would be 2*B right?
not the other way around?
 
aifan said:
But A takes longer than B it takes twice as long as B does so A would be 2*B right?
not the other way around?

No. A takes twice as long so only makes half as many widgets as B. You want widgets not time.
 
okay I got it now! I made a stupid error Thank you!
 
  • #10
aifan said:
okay I got it now! I made a stupid error Thank you!

I made the same mistake. :redface:
 

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