Question

A group of friends is addressing wedding invitations. Casey can address 22 envelopes in one hour, Anne can address 48 envelopes in two hours, and Paula can address 62 envelopes in three hours. About how long will it take them to address 420 envelopes?
A.
19.09 hours
B.
22.00 hours
C.
6.30 hours
D.
7.24 hours

Answer 1

To find out how long it will take Casey, Anne, and Paula to address 420 envelopes, we first need to determine their rates of addressing envelopes per hour.

1. **Casey's Rate:**
- Casey addresses 22 envelopes in 1 hour.
- Rate = 22 envelopes/hour.

2. **Anne's Rate:**
- Anne addresses 48 envelopes in 2 hours.
- Rate = 48 envelopes / 2 hours = 24 envelopes/hour.

3. **Paula's Rate:**
- Paula addresses 62 envelopes in 3 hours.
- Rate = 62 envelopes / 3 hours ≈ 20.67 envelopes/hour.

Now, let's add their rates together to find the combined rate:

- Combined rate = Casey's rate + Anne's rate + Paula's rate
- Combined rate = 22 + 24 + 20.67 = 66.67 envelopes/hour.

Next, we can find out how long it will take them to address 420 envelopes using the formula:

\[
\text{Time} = \frac{\text{Total Envelopes}}{\text{Combined Rate}}.
\]

Substituting the values we have:

\[
\text{Time} = \frac{420 \text{ envelopes}}{66.67 \text{ envelopes/hour}} \approx 6.30 \text{ hours}.
\]

Therefore, it will take them approximately 6.30 hours to address 420 envelopes.

The answer is **C. 6.30 hours**.