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At Supersonic Corporation, the time required for a machine

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At Supersonic Corporation, the time required for a machine

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Source: Manhattan Prep

At Supersonic Corporation, the time required to complete a job is determined by the formula: $$t=\sqrt{w}+\sqrt{(w-1)},$$ 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?
$$\text{A. }\frac{6}{7-\sqrt{3}}$$
$$\text{B. }\frac{1}{2}(\sqrt{8}+\sqrt{6})$$
$$\text{C. }\frac{1}{3}(6-\sqrt{3})$$
$$\text{D. }3(\sqrt{3}+\sqrt{2})$$
$$\text{E. }\sqrt{8}+2\sqrt{7}+\sqrt{6}$$
The OA is B

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Junior | Next Rank: 30 Posts Default Avatar
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t1= $$\sqrt{8}+\sqrt{7}\ $$
t2= $$\sqrt{7\ }+\sqrt{6}$$

1/t=(1/t1)+(1/t2)
Before plugging in the values, its more efficient to rationalize the values here itself. So t1 becomes $$\sqrt{8\ }-\sqrt{7}$$ and t2= $$\sqrt{7}-\sqrt{6}$$.

t=1/ $$\sqrt{8}-\sqrt{6}$$

Now rationalizing this value we get
t= $$\frac{\sqrt{8}+\sqrt{6}}{2}$$

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