Respuesta :
Answer:
It would take [tex]4\frac{4}{17}[/tex] or 4.24 hours to oil the lanes if they work together.
Step-by-step explanation:
Given:
Time to oil the lanes by Jimmy alone = 8 hours
Time to oil the lanes by Perry alone = 9 hours
Now, let the time taken by both working together be 'x' hours.
Part of the work done in 1 hour by Jimmy alone = [tex]\frac{1}{8}[/tex]
Part of the work done in 1 hour by Perry alone = [tex]\frac{1}{9}[/tex]
Part of the work done in 1 hour by Jimmy+Perry together = [tex]\frac{1}{x}[/tex]
Now, total work in 1 hour is given as:
[tex]\frac{1}{8}+\frac{1}{9}=\frac{1}{x}\\\\\frac{1\times 9}{8\times 9}+\frac{1\times 8}{8\times 9}=\frac{1}{x}\\\\\frac{9+8}{72}=\frac{1}{x}\\\\\frac{17}{72}=\frac{1}{x}\\\\\textrm{Doing cross product, we get:}\\\\17x=72\\\\x=\frac{72}{17}=4\frac{4}{17}\ hours[/tex]
Therefore, it would take [tex]4\frac{4}{17}[/tex] or 4.24 hours to oil the lanes if they work together.
