Question

I need help with this one please thanks

Answer 1

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.