Answers:
Emmanuel had worked for 52 minutes
and had added 416 links
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Explanation:
x = number of minutes Emmanuel has worked
y = number of links in the chain mail
Since Allesia started 20 minutes after Emmanuel, this means that she has worked for x-20 minutes (i.e. 20 minutes less time compared to x).
The equation for Emmanuel is
y = 8x
because he adds 8 links per minute.
Meanwhile, Allesia adds 13 links per minute and has worked for x-20 minutes. So her equation is
y = 13(x-20)
For each equation set up, I'm using the idea that
amount done = (rate)*(number of minutes)
It's similar to the distance=rate*time equation
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To find out when they'll have same amount done, we set the two right hand sides equal to one another. Then solve for x.
8x = 13(x-20)
8x = 13x-260
8x-13x = -260
-5x = -260
x = -260/(-5)
x = 52
Emmanuel had worked for 52 minutes and has added y = 8x = 8*52 = 416 links.
Allesia started 20 minutes later, so she works for 20 minutes less time. She works for x-20 = 52-20 = 32 minutes and does so at a rate of 13 links per minute. She has 13*32 = 416 links as well. Both people have the same number of links to confirm our answers.