Answer:
Emmanuel had worked for 52 minutes and had added 416 links.
(Khan Academy)
Explanation:
Let's use t to represent the number of minutes Emmanuel had worked and l to represent the number of links added to the chain mail.
We have two unknown values, so we can create and solve a system of two equations that represent this context.
Modeling the context:
Emmanuel added 8 links a minute, so for Emmanuel:
l=8t
Allesia worked for 20 minutes less than Emmanuel did, so she worked t-20. Allesia added 13 links a minute, so for Allesia:
l=13(t-20)
Now we have the following system of equations to represent our situation:
l=8t
l=13(t-20)
Solving for t by substituting
Let's substitute the value of l from the second equation into the first equation.
l=8t
13(t-20)=8t
13t-260=8t
5t-260=0
5t=260
t=52
Allesia catches up to Emmanuel after Emmanuel had worked 52 minutes.
Solving for l by substituting
We have one unknown left. Let's substitute the value we got for t back into one of the equations to solve for l.
l=8t
l=8(52)
l=416
Emmanuel had added 416 links.
Emmanuel had worked for 52 minutes and had added 416 links.