Answer:
D
Explanation:
Let's say that we have x amount of hours.
Casey addresses 22 envelopes per hour. Another way of writing this is that for x hours, Casey addresses 22 envelopes. Therefore, given x hours, Casey addresses 22 * x envelopes.
Anne can address 48 envelopes in 2 hours. It is important to note that this is for 2 hours. To make this per 1 hour, we can write
48 envelopes = 2 hours
divide both sides by 2
24 envelopes = 1 hour.
Therefore, given x hours, Anne addresses 24 * x envelopes.
Paula can address 62 envelopes in 3 hours, so
62 envelopes = 3 hours
divide both sides by 3
62/3 envelopes = 1 hour
Given x hours, Paula can address 62/3 * x envelopes.
Adding all of these up, given x hours, the group of friends can address
22 * x + 24 * x + 62/3 * x envelopes. Because the variables are all the same (x), we can add up the coefficients, resulting in
(22 + 24 + 62/3) * x = (46 + 62/3) * x envelopes given x hours
We want to figure out the amount of hours (x) for 420 envelopes. The total amount of envelopes is equal to (46 + 62/3) * x, so we set 420 equal to that, resulting in
(46 + 62/3) * x = 420
divide both sides by (46 + 62/3) to isolate x
420 / (46 + 62/3) = x
= 6.3 hours