Answer:
New computer will take 33.28 hours to complete the calculation by itself.
Step-by-step explanation:
Let the time taken by the new computer to complete the calculation = x hours
Per hours work done by the new computer = [tex]\frac{1}{x}[/tex]
Time taken by the older computer to complete the calculation = (x + 11) hour
Per hour work done by old computer = [tex]\frac{1}{(x+11)}[/tex]
When both the computers work together they complete the work in 19 hours.
Therefore, per hour work done by both together = [tex]\frac{1}{19}[/tex]
We per hour work done by both individually = per hour work done by both together
[tex]\frac{1}{x}+\frac{1}{x+11}=\frac{1}{19}[/tex]
[tex]\frac{x+x+11}{x(x+11)}=\frac{1}{19}[/tex]
[tex]\frac{2x+11}{x(x+11)}=\frac{1}{19}[/tex]
38x + 209 = x² + 11x
x² - 27x - 209 = 0
By quadratic formula,
x = [tex]\frac{27\pm \sqrt{(-27)^{2}-4\times 1\times (-209)}}{2}[/tex]
x = [tex]\frac{27\pm \sqrt{729+836}}{2}[/tex]
x = [tex]\frac{27\pm \sqrt{1565}}{2}[/tex]
x = [tex]\frac{27\pm 39.56}{2}[/tex]
x = 33.28 hours
Therefore, new computer will take 33.28 hours to complete the calculation by itself.
