Explanation

“Cheat” off the easier quantity.

In 40 minutes (from Quantity B), Rachel would assemble 40 ÷ 10 = 4 brochures and Terry would assemble 40 ÷ 8 = 5 brochures, for a total of 4 + 5 = 9 brochures.

Thus, Quantity A is also 40, and the two quantities are equal.
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1/10 + 1/8 = 9/T = Number of Brochure / Time

8/80 + 10/80 = 9/T

18/80 = 9/T

T=40
SO, ANSWER IS C

Rachel's rate is 1/10 (1 brochure per 10 minutes)

Terry's rate is 1/8 (1 brochure per 8 minutes)

Since the question asks us to find the number of minutes it will take Rachel and Terry, working together, to assemble 9 brochures we add the two rates together:
(1/10 + 1/8) = 9/40

9 brochures every 40 minutes. Therefore it will take 40 minutes to complete 9 brochures, which is the same as quantity B and thus the answer is C.

Additionally, you can use the following equation:

W = rate * time

Plug in 9 for W, 9/40 for the rate (combined rate of Terry and Rachel) and solve for Time.

Solving for Time yields 40 minutes to create 9 brochures.

If they are working together, total time taken is given by this formula:

\(T = \frac{a*b}{(a+b)}\)
and put a = 10 and b = 8 min
>> \(T = \frac{40}{9}\)
This is time required to produce 1 brochure .
But we need to calculate to produce 9 such brochure, multiplying with 9 yields 40. Hence both the column are equal.
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