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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?

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12 Nov 2014, 11:12

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"Three medical experts, working together at the same constant rate, can write an anatomy textbook in 24 days." This means that the rate of each individual doctor is 1/(3*24).

If n is the number of doctors needed to complete the work in 9 days, we have n/(3*24)*9=1. Therefore, n=8.

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12 Nov 2014, 11:38

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Answer choices A and B make no sense so we are quickly down to C, D, E.

Since each worker works at the same rate, I tried to figure out what fraction each worker was doing each day. Each worker must have been writing 1/72 of the textbook each day for the 24 days. So now we need to figure out how many it takes to write it in 9 days.

5 additional writers means that each day 8 writers are collectively writing 8/72 (1/9th) of the textbook.

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.

Re: Three medical experts, working together at the same constant rate, can [#permalink]

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05 Sep 2015, 10:29

this is a case of simple unitary method. Since all the experts have the same rate of work we don't need to calculate the rate. The values provided may be written as : Let the work ie to write the books be 1. No of Med Exp Amount of Work Days to finish the work 3 1 24 x 1 9 x = (3 * 1 * 24)/ 9 = 8

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26 Aug 2017, 09:51

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Three medical experts, working together at the same constant rate, can [#permalink]

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26 Aug 2017, 10:00

Since 3 medical experts working at a constant rate write a textbook in 24 days.

Lets assume that the book has 72(3*24) pages Now, each of these experts must write 1 page a day

Since x additional experts are added to write the same book in 9 days, \(\frac{72}{9} = 8\) pages need to be written in a day. We know that the existing 3 experts write 3 of those pages, leaving 5 pages to be written everyday.

So, we will need 5 additional experts to write the book(Option C) _________________

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