Answer:
[tex]4\frac{7}{8}\text{ minutes}[/tex]
Step-by-step explanation:
Let x be the number of minutes after which both sides have equal number of feet painted,
∵ One side of the fence is painted by Benito,
His speed = 15 ft/min
So, the number of feet painted in one side after x minutes = 15x,
Now, second side of the fence is painted by Taylor,
The feet he already painted = [tex]19\frac{1}{2}[/tex],
Taylor's speed = 11 ft/min
Thus, the number of feet painted in second side after x minutes = [tex]19\frac{1}{2}+11x[/tex],
[tex]15x = 19\frac{1}{2}+11x[/tex]
[tex]4x = 19\frac{1}{2}[/tex]
[tex]4x = \frac{39}{2}[/tex]
[tex]\implies x = \frac{39}{8}=4\frac{7}{8}\text{ minutes}[/tex]
Hence, it will take [tex]4\frac{7}{8}[/tex] minutes for both sides to have an equal number of feet painted.
