Janet, an experienced shipping clerk, can fill a certain order in 5 hours. Jim, a new clerk, needs 7 hours to do the same job. Working together, how long will it take them to fill the order?
To solve this problem, we can use the formula for working together:
1/T = 1/A + 1/B
where T is the time it takes to do the job together, A is the time it takes for Janet to do the job alone, and B is the time it takes for Jim to do the job alone.
In this case, A = 5 hours and B = 7 hours.
Plugging in the values, we get:
1/T = 1/5 + 1/7
To solve for T, we can find the common denominator:
1/T = (7 + 5) / (5*7)
1/T = 12/35
Now we can solve for T by taking the reciprocal:
T = 35/12
Thus, it will take them approximately 2.92 hours (or 2 hours and 55 minutes) to fill the order together.
To find out how long it will take them to fill the order working together, we can use the formula for the combined work rate of two people.
The formula is: 1/(time taken by Janet to complete the job) + 1/(time taken by Jim to complete the job) = 1/(time taken by both working together to complete the job).
Let's calculate:
Janet can fill the order in 5 hours, so her work rate is 1/5.
Jim can fill the order in 7 hours, so his work rate is 1/7.
Let's plug these values into the formula:
1/5 + 1/7 = 1/(time taken by both working together to complete the job)
To solve for the time taken by both working together, we need to find the reciprocal of the sum of the two work rates and then simplify.
1/5 + 1/7 = (7 + 5)/35 = 12/35
Therefore, the reciprocal is 35/12.
So, it will take them 35/12 hours to fill the order working together.
As a decimal, this is approximately 2.917 hours, or 2 hours and 55 minutes.
To find how long it will take Janet and Jim to fill the order when working together, we can use the concept of "work rate."
Let's first find the work rate of each clerk:
Janet can fill the order in 5 hours, so she completes 1/5th of the order in 1 hour. Therefore, Janet's work rate is 1/5.
Jim can fill the order in 7 hours, so he completes 1/7th of the order in 1 hour. Therefore, Jim's work rate is 1/7.
Now, to find the combined work rate of Janet and Jim, we simply add their individual work rates. So, the combined work rate is 1/5 + 1/7.
To determine the time it will take them to complete the order together, we take the reciprocal of the combined work rate. In other words, we divide 1 by the combined work rate: 1 / (1/5 + 1/7).
To simplify this fraction, we first find a common denominator, which is 35 in this case. So, the fraction becomes: 1 / (7/35 + 5/35).
Next, we add the fractions in the denominator: 1 / (12/35).
To divide by a fraction, we multiply by its reciprocal. So, we can multiply 1 by the reciprocal of 12/35: 1 * (35/12).
Multiplying across, we get 35/12.
Therefore, it will take Janet and Jim approximately 35/12 hours to fill the order together, which is approximately 2.92 hours or 2 hours and 55 minutes.