Sue​, an experienced shipping​ clerk, can fill a certain order in 5 hours. Felipe​, a new​ clerk, needs 7 hours to do the same job. Working​ together, how long will it take them to fill the​ order?

Answer 1

the underlying formula that you want to use to solve this one is

total time = 1 / combined rate

in this case we have

combined rate = 1/5 + 1/7 = 7/35 + 5/35 = 12/35 orders/hour

meaning that

total time = 1 / (12/35) = 35/12 = 2.92

so if they work together it will take them approximately 2.92 hours to fill the order, which is equal to 2 hours and 55 minutes

Answer 2

Hi Sasannah, thanks for your question!

1) Start with the equation for combined work: (1/Time of Worker A)+(1/ Time of Worker B)=(1/Total Time)

2) Plug in values: 1/5+1/7=1/Total time

3) Get Fractions to Common Denominator: 7/35+5/35=1/Total

4) Solve: 12/35=1/Total Time

5) Simplify: 35/12=Total Time

Answer: 2.92 hours combined time to complete the task.

Answer 3

Hello Sassanah,

Let's solve this problem using the concept of the work rate.

Sue's work rate is 1 job per 5 hours, and Felipe's work rate is 1 job per 7 hours.

When they work together, their work rates are combined. So, the combined work rate is the sum of their individual work rates:

Sue's work rate + Felipe's work rate = 1/5 + 1/7

To add these fractions, we need to find a common denominator, which is 35. So, we get:

7/35 + 5/35 = 12/35

This means that together, they complete 12/35 of the job per hour.

To find out how long it will take them to complete the job together, we can divide the total work (1 job) by their combined work rate:

Time taken = Total work / Combined work rate

Time taken = 1 / (12/35)

Time taken = 35/12

Now, we need to convert 35/12 to hours and minutes:

When 35 is divided by 12, it gives 2 with a remainder of 11.

35/12 = 2 11/12

This is 2 hours and 11/12 of an hour which is 55 minutes.

So, it will take Sue and Felipe approximately 2 hours and 55 minutes to fill the order together.

Answer 4

Hi Sasannah,

1. Let W represent the amount of work (i.e. filling the order)
2. The amount of work Sue is able to do each hour is W/5
3. The amount of work Felipe can do each hour is W/7
4. The total amount of work they can do together in one hour (or 60 minutes) is W/5 + W/7 = 60
5. Simplify the equation by multiplying the LCD (35): 7W + 5W = 2100
6. Combine terms: 12W = 2100
7. Divide by 12: W = 175
8. Together it will take them 175 minutes (or 2 hours and 55 minutes) to do the same amount of work to fill the order.

I hope this helps you!

Answer 5

First, we determine Sue and Felipe's individual work rates:

1. Sue can complete the order in 5 hours, so her work rate is 1/5​ of the order per hour.
2. Felipe can complete the order in 7 hours, so his work rate is 1/7 of the order per hour.

Working together, their combined work rate is the sum of their individual work rates:

1. Combined work rate = 1/5 + 1/7 = 12/35
2. This is saying that when they're working together, they can complete 12/35 of the order per hour.

To find the total time it takes them to complete one full order, we take the reciprocal of their combined work rate (i.e., doing the reverse of the first step):

1. Total time = 35/12 hours

Therefore, Sue and Felipe working together will take approximately 2.92 hours to fill one order.