Respuesta :

notice, the object is covering in 1 hour, 10 and 1/10 miles, thus

[tex]\bf \begin{array}{ccll} miles&hours\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 10\frac{1}{10}&1\\\\ 4\frac{9}{10}&h \end{array}\implies \cfrac{10\frac{1}{10}}{4\frac{9}{10}}=\cfrac{1}{h}\implies \cfrac{\frac{10\cdot 10+1}{10}}{\frac{4\cdot 10+9}{10}}=\cfrac{1}{h}[/tex]

[tex]\bf \cfrac{\quad\frac{101}{10} \quad }{\frac{49}{10}}=\cfrac{1}{h}\implies \cfrac{101}{10}\cdot \cfrac{10}{49}=\cfrac{1}{h}\implies \cfrac{1010}{490}=\cfrac{1}{h}\implies 1010h=490 \\\\\\ h=\cfrac{490}{1010}\qquad \qquad \textit{about 29 minutes and 6 and a half seconds}[/tex]
dfrancolopera

Answer:

Then, the object will take 29.11 min to travel [tex]4\frac{9}{10} miles[/tex]

Step-by-step explanation:

When an object is moving at a steady speed, we can calculate the time it would take to travel a given distance using the following formula:

[tex]time=\frac{distance}{speed}[/tex] (equation 1)

In this particular, both the given speed and distance are mixed fractions so we'll first convert them into improper fractions to operate more easyly:

[tex]speed=10 \frac{1}{10} \frac{mi}{h}=\frac{(10*10)+1}{10}\frac{mi}{h}=\frac{101}{10}\frac{mi}{h}[/tex]

[tex]distance=4 \frac{9}{10} mi=\frac{(4*10)+9}{10}mi=\frac{49}{10}mi[/tex]

So, now we can calculate the time using the equation 1:

[tex]time=\frac{distance}{speed}=\frac{\frac{49}{10}mi}{\frac{101}{10}\frac{mi}{h}}=\frac{49*10}{101*10}h[/tex]

[tex]time=\frac{49}{101}h=0.49h[/tex]

And, if we want the result in minutes:

[tex]time=\frac{49}{101}h*\frac{60 min}{1 h}=29.11 min[/tex]

Then, the object will take 29.11 min to travel [tex]4\frac{9}{10} miles[/tex]