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You can stuff envelopes twice as fast as your friend. Together, you can stuff 6750 envelopes in 4.5 hours. How long would it take for each of you working alone to complete the job individually?

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If you're twice a fast then... we'll divide 6750 by 3, that equals 2250. 
Equation.. y=your friend and you would be 2y cuz you're twice as fast.
y+2y=6750, 
3y=6750
y=2250

Your friend stuffed 2250 in 4.5 hrs.
You (twice as fast) stuffed 4500 in 4.5 hrs.


Working alone, your friend can stuff 2250 in 4.5hrs so it would take 13.5hrs to stuff 6750. 
Equation.. (6750/2250) x 4.5hrs = 13.5hrs

You can 4500 in 4.5hrs so it would take you 6.75 hrs to stuff 6750.
Equation.. (6750/4500) x 4.5hrs = 6.75 hrs.

Answer:

13.5 hours to your friend, and 6.75 to you.

Step-by-step explanation:

First, we have to find the individual ratio, how many envelopes per hour they can stuff.

So, we now that you can stuff envelopes twice faster than your friend, and both of you, that is, the sum, results in 6750 envelopes in 4.5 hours. The equation would be:

[tex]x+2x=\frac{6750 \ envelopes}{4.5 \ hour}\\3x=\frac{6750 \ envelopes}{4.5 \ hour}\\x=\frac{6750 \ envelopes}{3(4.5) \ hour}=500 \ envelopes/hr.\\2x=1000 \ envelopes/hour.[/tex]

Now we apply the rule of three to find the time to stuff 6750 envelopes.

If your friend can stuff 500 envelopes per hour, how much time would take 6750?

[tex]x=6750\frac{1}{500}=13.5 hours[/tex]

So, it would take 13.5 hours to your friend, to stuff all envelopes alone.

Now, if you can envelope 1000 envelopes per hour, that is, twice than your friend. How much time would take to you to stuff 6750 envelopes?

[tex]x=6750\frac{1}{1000}=6.75 hours[/tex]

It would take to you 6.75 hours to stuff all 6750 envelopes alone.

Therefore, the answers are 13.5 hours to your friend, and 6.75 to you.

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