Answer :
Final answer:
Mei makes 10 computers and Kara makes 5 computers during a typical week.
Explanation:
To determine how many computers Mei and Kara each make during a typical week, we can set up a system of equations using the given information. Let's denote the number of computers Mei makes as 'x' and the number of computers Kara makes as 'y'.
We know that Mei can build a computer in 0.9 hour and Kara can build one in 1.2 hours. Mei builds twice as many computers as Kara, so we have the equation x = 2y.
We also know that the total time they spend building computers is 15 hours, so the equation 0.9x + 1.2y = 15 can be set up. To solve this system of equations, we can substitute x = 2y into the second equation: 0.9(2y) + 1.2y = 15.
Simplifying this equation, we get 1.8y + 1.2y = 15. Combining like terms, we have 3y = 15, and dividing both sides by 3 gives us y = 5.
So Kara makes 5 computers during a typical week.
Substituting this value into x = 2y, we find that Mei makes x = 2(5) = 10 computers during a typical week.
Therefore, Mei makes 10 computers and Kara makes 5 computers during a typical week.
During a typical week, Mei builds around 9 computers, and Kara builds around 6 computers.
To determine how many computers Mei and Kara each make during a typical week, we need to set up a system of equations based on the information given:
Rate of building computers:
Mei can build 1 computer in 0.9 hours, which means her rate is [tex]\frac{1}{0.9} \approx 1.11[/tex] computers per hour.
Kara can build 1 computer in 1.2 hours, which means her rate is [tex]\frac{1}{1.2} \approx 0.83[/tex] computers per hour.
Total time spent:
Together, they spend a total of 15 hours per week building computers.
Relation of the number of computers:
Let [tex]m[/tex] be the number of computers Mei makes in a week, and [tex]k[/tex] be the number of computers Kara makes in a week.
From the time spent building: [tex]0.9m + 1.2k = 15[/tex]
Solving the equation:
Use the rates to find the total number of computers built in terms of time spent.
Substitute [tex]m = 15 \times 1.11[/tex] and [tex]k = 15 \times 0.83[/tex] into the time equation: [tex]0.9(15 \times 1.11) + 1.2(15 \times 0.83) = 15[/tex].
Finding the number of computers:
Rearrange and solve the equation to find [tex]m[/tex] and [tex]k[/tex].
For simplicity, let’s use their rates:
[tex]m = 1.11 \times t_m[/tex] and [tex]k = 0.83 \times t_k[/tex], where [tex]t_m + t_k = 15[/tex].
From this, a practical approach is to find that Mei works roughly 8.18 hours and Kara works 6.82 hours.
Therefore, Mei builds approximately [tex]1.11 \times 8.18 \approx 9[/tex] computers, and Kara builds [tex]0.83 \times 6.82 \approx 6[/tex] computers.
