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
22.00 hours
B. 7.24 hours
C 19.09 hours
D. 6.30 hours

Answer 1

D. 6.30 hours

Explanation:

The total rate of the friends working together is the sum of their rates. That rate can be used to find the amount of time for the specific job.

Total Rate

Rates are given in terms of envelopes in a time period. We can divide the number of envelopes by the time period to find the rate in envelopes per hour:

• Casey: (22 envelopes)/(1 h) = 22 envelopes/h
• Anne: (48 envelopes)/(2 h) = 24 envelopes/h
• Paula: (62 envelopes)/(3 h) = 20 2/3 envelopes/h

The rate when all three work together is ...

(22 +24 +20 2/3) envelopes/h = 66 2/3 envelopes/h

Total time

The time can be found by dividing the quantity by the rate:

(420 envelopes)/(66 2/3 envelopes/h) = (420/(200/3)) h

= 1260/200 h = 6.30 h

It will take about 6.30 hours for them to address 420 envelopes.