Respuesta :
Time taken by jerry alone is 10.1 hours
Time taken by callie alone is 8.1 hours
Solution:
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 [tex]\frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }[/tex]
If they work together they can do the entire prospectus in five hours
[tex]\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}[/tex]
On cross-multiplication we get,
[tex]\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}[/tex]
[tex]\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}[/tex]
On cross multiplication ,we get
[tex]\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}[/tex]
using quadratic formula:-
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
[tex]x=\frac{12 \pm \sqrt{144-40}}{2}[/tex]
[tex]\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}[/tex]
If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative value
Let us take a = 10.1
So time taken by jerry alone = a = 10.1 hours
Time taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours
