A firm advertises for workers to address envelopes. Priscilla says she will work 100 hours. Herb will work for 80 hours. If each can address 10,000 envelopes in the time they work, how long would it take them to address 10,000 envelopes if they work together?
i am lost, can you show steps with the answer
Certainly! Let's break it down step by step.
1. Priscilla can address 10,000 envelopes in 100 hours, so her rate is 10,000 envelopes / 100 hours = 100 envelopes per hour.
2. Herb can address 10,000 envelopes in 80 hours, so his rate is 10,000 envelopes / 80 hours = 125 envelopes per hour.
3. To find their combined rate, we add their individual rates: 100 envelopes per hour + 125 envelopes per hour = 225 envelopes per hour.
4. Now we can determine how long it would take them to address 10,000 envelopes if they work together. We divide the total number of envelopes (10,000) by their combined rate (225 envelopes per hour):
Time = 10,000 envelopes / 225 envelopes per hour
Time = 44.44 hours
So, it would take Priscilla and Herb approximately 44.44 hours to address 10,000 envelopes if they work together.
Certainly! Let's break down the problem step by step:
Step 1: Find the total number of hours they will work together.
To find the total number of hours, we add Priscilla's hours and Herb's hours together:
100 hours + 80 hours = 180 hours
Step 2: Find the total number of envelopes they can address per hour when working together.
Since each person can address 10,000 envelopes in the time they work, we need to find how many envelopes they can address per hour:
10,000 envelopes / 180 hours = 55.56 envelopes per hour (rounded to two decimal places)
Step 3: Determine how long it would take them to address 10,000 envelopes if they work together.
Now that we know they can address 55.56 envelopes per hour, we can find the time it would take to address 10,000 envelopes:
10,000 envelopes / 55.56 envelopes per hour ≈ 179.99 hours (rounded to two decimal places)
Therefore, it would take them approximately 179.99 hours (or around 180 hours) to address 10,000 envelopes if they work together.
To find out how long it would take Priscilla and Herb to address 10,000 envelopes if they work together, we need to determine their combined rate of work first.
Priscilla can address 10,000 envelopes in 100 hours, which means she can address 100 envelopes per hour (10,000 envelopes ÷ 100 hours = 100 envelopes per hour).
Similarly, Herb can address 10,000 envelopes in 80 hours, so his rate of work is 125 envelopes per hour (10,000 envelopes ÷ 80 hours = 125 envelopes per hour).
To find their combined rate of work, we add their individual rates together. So, the combined rate is 100 + 125 = 225 envelopes per hour.
Now, since we know the combined rate, we can calculate the time it would take for Priscilla and Herb to address 10,000 envelopes if they work together.
Let's set up a proportion using the combined rate and the number of envelopes to address:
225 envelopes / 1 hour = 10,000 envelopes / x hours.
To solve for x, we can cross-multiply and then divide:
225x = 10,000.
x = 10,000 / 225.
x ≈ 44.4.
Therefore, it would take approximately 44.4 hours for Priscilla and Herb to address 10,000 envelopes if they work together.
If they take x hours together,
1/x = 1/100 + 1/80
This is just a typical work problem. Forget the 10,000 envelopes. It's just 1 job. P can do 1/100 of the job in an hour, and H can do 1/80. So, add up the amounts they do.