You work in retail. In the past you inventoried and shelved the weekly UPS shipment in 2 hours. Your co-worker usually takes 3 hours to do the UPS shipment. How long will it take the two of you working together to finish this week’s UPS shipment?
1)What units are you looking for?
Choose a variable to represent this value?
2)Should your answer be more or less than 2 hours? Why?
3)What fraction of the job can you do in 1 hour working alone?
This is your work rate.
4)What fraction of the job can your co-worker do in 1 hour working alone? This is his work rate.
5)Using the variable you chose, what fraction of the job can you two do in 1 hour working together?
This is your combined work rate.
6)Write an equation.
7)Describe at least two ways to solve this equation.
We can finish the UPS shipment in ________ ________ working together.
Your teacher has laid out a solution path that is very thinking. First, consider this solution.
in six hours, you could do three shipmehnts, and coworker could do two shippments.
Both of you could do 5shipmeths in 6 hrs, and your combined rate is 5/6 shipment/hr, so it takes you 6/5 of an hour, or 6*60/5 min= 72 min
Now for the innane questions. I would never teach this method.
1. you are looking for time.
2.guess yourself.
3. in one hour, you can do .5 of the job
4. in one hour, she can do .3333 of the job.
5.you can do .833333 of the job in an hour.
6. time=1 shipment/(.83333 ship/hr)=1.2 hr=72 min.
you are correct Lena, however, in this case, kids have a hard time with the concept, and the teacher is asking for a solution analysis that is hard for many kids to grasp. I showed him an easier way.
Thanks.
1) The units we are looking for are the number of hours it will take the two of you to finish the UPS shipment.
Let's represent this value with the variable "x".
2) The answer should be less than 2 hours because you and your co-worker are working together, so you should be able to finish the task faster than if you were working alone.
3) To determine your work rate, we need to find the fraction of the job you can do in 1 hour working alone. Since you can inventory and shelve the weekly UPS shipment in 2 hours, your work rate is 1/2 or 1 job per 2 hours.
4) To determine your co-worker's work rate, we need to find the fraction of the job he can do in 1 hour working alone. Since your co-worker takes 3 hours to inventory and shelve the UPS shipment, his work rate is 1/3 or 1 job per 3 hours.
5) To find the combined work rate of you and your co-worker, we add your individual work rates together. So, your combined work rate is (1/2) + (1/3) or (3 + 2) / 6 which simplifies to 5/6 or 1 job per 6/5 = 1.2 hours.
6) The equation for this problem is: (1/2)x + (1/3)x = 1, where "x" represents the number of hours it will take the two of you to finish the UPS shipment.
7) There are two ways to solve this equation:
- Multiply both sides of the equation by 6 to eliminate the denominators. This will give you 3x + 2x = 6. Combine like terms to get 5x = 6. Divide both sides by 5 to solve for x, which gives you x = 6/5 or 1.2 hours.
- Another way is to find a common denominator for the fractions (2 and 3), which is 6. Then you can rewrite the equation as (3/6)x + (2/6)x = 1. Add the fractions on the left side to get (5/6)x = 1. Multiply both sides of the equation by (6/5) to solve for x, which gives you x = 6/5 or 1.2 hours.
We can finish the UPS shipment in 1.2 hours working together.