Q:

Terry and Callie do word processing. For a certain prospectus Callie can prepare it two hours faster than Terry can. If they work together they can do the entire prospectus in five hours. How long will it take each of them working alone to repair the prospectus? Round answers to the nearest 10th of an hour

Accepted Solution

A:
Time taken by jerry alone is 10.1 hoursTime taken by callie alone is 8.1 hoursSolution:Given:- For a certain prospectus Callie can prepare it two hours faster than Terry can Let the time taken by Terry be "a" hours So, the time taken by Callie will be (a-2) hours Hence, the efficiency of Callie and Terry per hour is $$\frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }$$If they work together they can do the entire prospectus in five hours$$\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}$$On cross-multiplication we get,$$\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}$$$$\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}$$On cross multiplication ,we get$$\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}$$using quadratic formula:-$$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$$$x=\frac{12 \pm \sqrt{144-40}}{2}$$$$\begin{array}{l}{x=\frac{12 \pm \sqrt{144-40}}{2}} \\\\ {x=\frac{12 \pm \sqrt{104}}{2}} \\\\ {x=\frac{12 \pm 2 \sqrt{26}}{2}} \\\\ {x=6 \pm \sqrt{26}=6 \pm 5.1} \\\\ {x=10.1 \text { or } x=0.9}\end{array}$$If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative valueLet us take a = 10.1So time taken by jerry alone = a = 10.1 hoursTime taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours