Respuesta :
Answer:
[tex]2\frac{2}{5}\ minutes[/tex]
Step-by-step explanation:
Convert mixed number to an improper fractions first
[tex]2\frac{1}{6}\frac{ft}{min}=\frac{2*6+1}{6}=\frac{13}{6}\frac{ft}{min}[/tex]
[tex]5\frac{1}{5}\ ft=\frac{5*5+1}{5}=\frac{26}{5}\ ft[/tex]
By proportion
[tex]\frac{(13/6)}{1}\frac{ft}{min} =\frac{(26/5)}{x}\frac{ft}{min}\\ \\ x=(26/5)/(13/6)\\ \\x=156/65\ min[/tex]
Convert to mixed number
[tex]\frac{156}{65}\ min=\frac{130}{65}+\frac{26}{65}=2+\frac{26}{65}=2+\frac{2}{5} =2\frac{2}{5}\ min[/tex]
The rate of speed is the rate at which the total distance is traveled in the time taken. The time taken by the ant to crawl a distance of [tex]5\dfrac{1}{5}[/tex] feet is [tex]2\dfrac{2}{5}[/tex] minutes.
What is rate of speed?
The rate of speed is the rate at which the total distance is traveled in the time taken. Rate of speed can be given as,
[tex]s_r=\dfrac{x}{t}[/tex]
Here, [tex]x[/tex] is the distance traveled by the object and [tex]t[/tex] is time taken but the object to cover that distance.
Given information-
The rate of speed of crawl of ant is [tex]2\dfrac{1}{6}[/tex] feet per minute.
Total distance is [tex]5\dfrac{1}{5}[/tex] feet.
As the total distance is [tex]5\dfrac{1}{5}[/tex] feet and the rate of speed of the crawl of ant is [tex]2\dfrac{1}{6}[/tex] . Hence the time can be calculated using above formula as,
[tex]s_r=\dfrac{x}{t}[/tex]
Put the values,
[tex]2\dfrac{1}{6} =\dfrac{5\dfrac{1}{5} }{t}[/tex]
[tex]\dfrac{13}{6} =\dfrac{\dfrac{26}{5} }{t}[/tex]
Solve for [tex]t[/tex],
[tex]t=\dfrac{26}{5} \times\dfrac{13}{6} \\t=\dfrac{26}{5}\\t=2\dfrac{2}{5}[/tex]
Hence the time taken by the ant to crawl a distance of [tex]5\dfrac{1}{5}[/tex] feet is [tex]2\dfrac{2}{5}[/tex] minutes.
Learn more about the rate of speed here;
https://brainly.com/question/359790
