Every week Linda must stuff 1000 envelopes. She can do the job by herself in 6hrs. If Laura helps, they get done in 5 1/2 hrs. How long would it take Laura to do the job herself?
Let Laura's time by herself be x.
The equation to solve is 1/6 + 1/x = 1/5.5 = 2/11
1/x = 2/11 -1/6 = 12/66 - 11/66 = 1/66
x = 66 hours (That's why Laura isn't much help)
m(m - 3) < 54
To solve this problem, we can use the concept of work rates. Let's denote Linda's work rate as L (in envelopes per hour) and Laura's work rate as X (in envelopes per hour).
Given that Linda can complete the job by herself in 6 hours, we have:
Linda's work rate = 1000 envelopes / 6 hours = 166.67 envelopes per hour
If Linda and Laura work together, they are able to complete the job in 5.5 hours, which gives us the equation:
(166.67 envelopes per hour + X envelopes per hour) * 5.5 hours = 1000 envelopes
Simplifying the equation:
(166.67 + X) * 5.5 = 1000
916.67 + 5.5X = 1000
Subtracting 916.67 from both sides of the equation:
5.5X = 1000 - 916.67
5.5X = 83.33
Dividing both sides of the equation by 5.5:
X = 83.33 / 5.5
X = 15.15
Therefore, Laura's work rate is approximately 15.15 envelopes per hour.
To find out how long it would take Laura to do the job by herself, we can use the equation:
Laura's work rate = 1000 envelopes / number of hours
Laura's work rate = 15.15 envelopes per hour
Number of hours = 1000 envelopes / 15.15 envelopes per hour
Simplifying the equation:
Number of hours = 65.97 hours
Hence, it would take Laura approximately 66 hours to do the job by herself.
To find out how long it would take Laura to do the job by herself, we can use the concept of rates.
Let's denote Linda's rate of stuffing envelopes per hour as L, and Laura's rate as R.
We know that Linda can stuff 1000 envelopes in 6 hours, so her rate is:
Linda's rate = 1000 envelopes / 6 hours = 166.67 envelopes/hour (rounded to two decimal places)
If Laura helps Linda, they can get the job done in 5 1/2 hours (which is equivalent to 5.5 hours). This means that their combined rate is:
Combined rate = 1000 envelopes / 5.5 hours = 181.82 envelopes/hour (rounded to two decimal places)
Now, let's use the information we have to find Laura's rate. We know that the combined rate is the sum of Linda's rate and Laura's rate:
Combined rate = Linda's rate + Laura's rate
Substituting the values we have:
181.82 envelopes/hour = 166.67 envelopes/hour + Laura's rate
To find Laura's rate, we can rearrange the equation:
Laura's rate = Combined rate - Linda's rate
Laura's rate = 181.82 envelopes/hour - 166.67 envelopes/hour
Laura's rate = 15.15 envelopes/hour
Since we now know Laura's rate, we can find out how long it would take her to stuff 1000 envelopes by dividing the total number of envelopes by her rate:
Time taken by Laura = 1000 envelopes / Laura's rate
Time taken by Laura = 1000 envelopes / 15.15 envelopes/hour
Time taken by Laura ≈ 65.93 hours
Therefore, it would take Laura approximately 65.93 hours to stuff 1000 envelopes if she works by herself.