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

In summary, the problem states that employee A takes twice as long as employee B to make a widget, and together they can make 15 widgets in a day. Using the equation rate = area/time, we can set up two equations: A = 2*B and A + B = 15. Solving for A, we get A = 2*B and A = 15 - B. Substituting 2*B in for A in the second equation, we get 2*B = 15 - B. Simplifying, we get B = 5 and A = 10, meaning that employee A makes 10 widgets per day.
  • #1
aifan
5
0

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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  • #2
aifan said:
...their rate together should be A + B = 15 widgets.

What is A equal to?
 
  • #3
A is equal to 2B.
I tries doing 2B + B = 15
which is 5 but that is solving for B not A
 
  • #4
Well you know what A + B equals to. So A = ?
 
  • #5
A = 15 - b
 
  • #6
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.
 
  • #7
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?
 
  • #8
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.
 
  • #9
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:
 

1. What is a rate in a word problem?

A rate in a word problem is a comparison of two quantities that have different units of measurement. It is often expressed as a ratio and represents how much one quantity changes in relation to another quantity.

2. How do you solve for the rate in a word problem?

To solve for the rate in a word problem, you need to identify the two quantities being compared and set up a ratio with those quantities. Then, use the information given in the problem to find the value of the missing quantity in the ratio, which represents the rate.

3. What are some common units used in rate problems?

Some common units used in rate problems include miles per hour, dollars per hour, gallons per minute, and items per hour. The specific units used will depend on the context of the problem.

4. Can the rate change in a word problem?

Yes, the rate can change in a word problem. Rates are often represented as variables, and they can vary depending on the situation. It is important to carefully read the problem and identify if the rate is constant or changing.

5. What are some real-world applications of rate problems?

Rate problems can be applied to many real-world situations, such as calculating the speed of a moving object, determining the cost per unit of a product, or finding the time it takes to complete a task. They are also commonly used in finance and economics to calculate interest rates and exchange rates.

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