Final answer:
Lauren stuffed 672 envelopes in an hour, while Thomas stuffed 720 envelopes in an hour. It would take Lauren and Thomas approximately 245 minutes to stuff a total of 2,604 envelopes at their current rates.
Step-by-step explanation:
Part A:
To find out how many envelopes Lauren stuffed in an hour, we first need to convert the minutes to hours. Since there are 60 minutes in an hour, we can find the number of envelopes Lauren stuffed in an hour by multiplying her rate per minute by 60. So, Lauren stuffed 56 envelopes in 5 minutes, which means her rate is 56/5 envelopes per minute. Multiplying this rate by 60 gives us 56/5 * 60 = 672 envelopes per hour. Therefore, Lauren stuffed 672 envelopes in an hour.
Similarly, Thomas stuffed 42 envelopes in 3.5 minutes, which means his rate is 42/3.5 envelopes per minute. Multiplying this rate by 60 gives us 42/3.5 * 60 = 720 envelopes per hour. Therefore, Thomas stuffed 720 envelopes in an hour.
Part B:
To find out how long it would take Lauren and Thomas to stuff a total of 2,604 envelopes at their current rates, we can add their rates and divide the total number of envelopes by their combined rate. Lauren's rate is 56 envelopes per 5 minutes, and Thomas' rate is 42 envelopes per 3.5 minutes. Adding their rates gives us 56/5 + 42/3.5 envelopes per minute. Simplifying this expression gives us 392/35 envelopes per minute. Dividing the total number of envelopes, 2,604, by their combined rate gives us 2604 / (392/35) minutes. Simplifying this expression gives us 7 * 35 = 245 minutes. Therefore, it would take Lauren and Thomas approximately 245 minutes to stuff a total of 2,604 envelopes at their current rates.