Bunuel wrote:
Tough and Tricky questions: Work Problems.
Three medical experts, working together at the same constant rate, can write an anatomy textbook in 24 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 9 days?
A. 2
B. 3
C. 5
D. 8
E. 15
Kudos for a correct solution. Official Solution:Three medical experts, working together at the same constant rate, can write an anatomy textbook in 24 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 9 days?A. 2
B. 3
C. 5
D. 8
E. 15
We are asked to determine how many
additional experts must be added to our team of 3 in order to decrease the time required to write an anatomy textbook from 24 days to 9 days.
We can plug in the values we are given into the work formula, \(w = rt\), where \(w\) is the amount of work done, \(r\) is the rate at which the work is performed, and \(t\) is the time it takes the work to be completed. In this case, \(w = 1\) (since there is one textbook), \(t = 24\), and \(r\) is unknown. Thus, the original situation can be represented by the formula: \(1 = (3r)(24) = 72r\). Note that we use \(3r\) because there are 3 people working, each at the same rate of \(r\).
We solve for \(r\) by dividing both sides by 72, leaving \(r = \frac{1}{72}\) book per day. This is the rate at which each expert works.
We use this value of \(r\) to solve for \(k\), the number of experts it would take to write a book in 9 days. In this new equation, \(w\) will still equal 1, \(r = \frac{1}{72}k\), and \(t = 9\). This gives us: \(1 = (\frac{1}{72}k)(9) = \frac{1}{8}k\). We solve for \(k\) by multiplying both sides by \(8\). We find that \(k = 8\). So it will take 8 experts to finish the book in 9 days.
Remember, though, that we are looking for the number of
additional experts. Since we already have 3 experts, in order to get 8, we need an additional \(8 - 3 = 5\) experts.
Answer: C.
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