Bunuel wrote:
Tough and Tricky questions: Work/Rate.
At Supersonic Corporation, the time required for a machine to complete a job is determined by the formula: , where w = the weight of the machine in pounds and t = the hours required to complete the job. If machine A weighs 8 pounds, and machine B weighs 7 pounds, how many hours will it take the two machines to finish one job if they work together?
A. \(\frac{6}{7-\sqrt{3}}\)
B. \(\frac{1}{2}(\sqrt{8}+\sqrt{6})\)
C. \(\frac{1}{3}(6-\sqrt{3})\)
D. \(3(\sqrt{3}+\sqrt{2})\)
E. \(\sqrt{8}+2\sqrt{7}+\sqrt{6}\)
I agree with manpreet's solution, but hopefully this adds a bit clarity:
First thing you need to know for this type of problem is the work problem rules (if you have
the Official Guide, look at section 4.4.2). The formula for solving work problems where two machines work together is:
\(\frac{1}{r} + \frac{1}{s} = \frac{1}{h}\)
r = number of hours it takes machine A to complete a unit;
s = number of hours it takes machine B to complete a unit;
h = number of hours it takes both machines working together
This video explains the simplification that Manpreet did.
[youtube]https://www.youtube.com/watch?v=1oiy9OjwxLg[/youtube]
Now that we have our new, simplified formula, we apply it to our current problem:
t(A) = time for machine A to complete a unit = r
t(B) = time for machine B to complete a unit = s
t(h) = time for both machines working together
(\(\sqrt{8}-\sqrt{8-1}\)) + (\(\sqrt{7}-\sqrt{7-1}\))
= (\(\sqrt{8}-\sqrt{7}\)) + (\(\sqrt{7}-\sqrt{6}\))
=(\(\sqrt{8}-\sqrt{6}\)) = \(\frac{1}{h}\)
Now, multiply by (\(\sqrt{8}+\sqrt{6}\)) / (\(\sqrt{8}-\sqrt{6}\)) so that you can simplify the answer to match the answer choices.
You found your answer, choice B.
You may be thinking: what if you don't know exactly how to factor these equations during the exam. It may end up taking a lot of time. I don't recommend it as the primary way, but if you can get close to the answer, but it isn't formatted in a way reflected by the answer choices, try to solve it out (if it can be done quickly) or approximate a number and find the answer choice that matches.
Alternatively, if you're REALLY short on time, you can try to eliminate some answer choices early on by partially solving the problem and thereby improve your chances of guessing correctly.