Question

Tiffany has a temp job at an office where she is helping them stuff envelopes for a big mailing. She doesn’t know how many envelopes they had already stuffed when she started helping them, but 20 minutes after she arrived they had stuffed a total of 400 envelopes, and 40 minutes after she arrived they had stuffed a total of 650 envelopes. At what rate, in envelopes per minute, have they been stuffing envelopes since Tiffany arrived?

Answer 1

To find the rate of stuffing envelopes since Tiffany arrived, we need to calculate the number of envelopes stuffed per minute. We can use the given information about the total number of envelopes stuffed after certain time intervals to find the rate at which they are being stuffed. Setting the rates at different time intervals equal to each other and solving the equation will give us the initial number of envelopes stuffed, which we can substitute back to find the rate.

Step-by-step explanation:

To find the rate at which envelopes are being stuffed since Tiffany arrived, we need to calculate the number of envelopes stuffed per minute. We can subtract the initial number of envelopes stuffed from the total number of envelopes stuffed after a certain time to find the number of envelopes stuffed in that time period. Then we divide that number by the time in minutes to get the rate. In this case, 40 minutes after Tiffany arrived, they had stuffed a total of 650 envelopes. So, the number of envelopes stuffed in 40 minutes is 650 - x, where x is the initial number of envelopes stuffed. Therefore, the rate is (650 - x) / 40 envelopes per minute.

Similarly, 20 minutes after Tiffany arrived, they had stuffed a total of 400 envelopes. So, the number of envelopes stuffed in 20 minutes is 400 - x. Therefore, the rate is (400 - x) / 20 envelopes per minute.

Since the rate is the same for both time periods, we can set the two rates equal to each other and solve for x: (650 - x) / 40 = (400 - x) / 20. Solving this equation will give us the initial number of envelopes stuffed, x. Once we have x, we can substitute it back into either rate equation to find the rate at which they are stuffing envelopes since Tiffany arrived.

Answer 2

To find the rate at which they have been stuffing envelopes since Tiffany arrived, subtract the number of envelopes stuffed 20 minutes later from the number of envelopes stuffed 40 minutes later. This gives the number of envelopes stuffed in 20 minutes, which can be used to determine the rate per minute.

Step-by-step explanation:

To find the rate at which they have been stuffing envelopes since Tiffany arrived, we need to determine the number of envelopes stuffed per minute.

To do this, we subtract the number of envelopes stuffed 20 minutes after Tiffany arrived from the number of envelopes stuffed 40 minutes after Tiffany arrived.

This gives us the number of envelopes stuffed in 20 minutes.

Number of envelopes stuffed in 20 minutes = 650 envelopes - 400 envelopes = 250 envelopes

Therefore, the rate at which they have been stuffing envelopes since Tiffany arrived is 250 envelopes per 20 minutes, which simplifies to 12.5 envelopes per minute.