Answer :
Final answer:
During a typical week, Mei builds 10 computers and Kara builds 5 computers. We use a system of equations based on their building rates and weekly work hours to calculate the number of computers built.
Explanation:
Calculating Computers Built per Week by Mei and Kara
To find out how many computers Mei and Kara make during a typical week, we first need to establish a system of equations based on the given information.
Mei can build a computer in 0.9 hours, and Kara can build one in 1.2 hours.
Let M represent the number of computers Mei builds in a week
K be the number of computers Kara builds in the same period
Given that Mei builds twice as many as Kara, we can write that as M = 2K.
One week, they spent a total of 24 hours building computers.
This can be represented as the equation 0.9M + 1.2K = 24.
Substituting M from the first equation into the second equation,
we get 0.9(2K) + 1.2K = 24, which simplifies to
3K = 24, solving for K, we get K = 8.
Therefore, M = 2K = 2 × 8 = 16.
In a typical week where they spend 15 hours building computers, we use the same approach.
We have 0.9M + 1.2K = 15. Substituting M into this equation from M = 2K, we get
0.9(2K) + 1.2K = 15,
simplifying to 3K = 15 and solving for K, we find K = 5.
Thus, Mei builds 10 computers (M = 2 × 5).