Question

Alaana is now grouped with two additional volunteers, zara and avery. avery works twice as fast as zara. altogether, alaana, zara, and avery construct the bins in a total of 10 hours. determine how long it takes zara and avery to individually contruct the bins.

Answer 1

Zara takes 15 hours to construct the bins individually, while Avery takes 7.5 hours.

Step-by-step explanation:

To determine how long it takes Zara and Avery to individually construct the bins, we can assign variables to represent their individual work rates. Let's say Zara's work rate is r, which means she can complete the job in 1/r hours. Since Avery works twice as fast as Zara, his work rate is 2r, and he can complete the job in 1/(2r) hours.

Now, we can set up an equation based on the given information. The combined work rate of Alaana, Zara, and Avery is 1/10 (since they complete the job in 10 hours), which can be expressed as (1/r + 1/(2r)) = 1/10.

Multiplying both sides of the equation by 10r will eliminate the fractions:

10 + 5 = r

r = 15

Therefore, Zara can individually construct the bins in 15 hours, and Avery can individually construct the bins in half that time, which is 7.5 hours.