If a train travels 70 miles per hour how long will it take it to travel 350 miles at this speed

1 answer:

4 0

Since the train travels at a rate of 70 miles/hour, the train will take 5 hours to have traveled a total of 350 miles. The missing information in the question you've proposed is the value of "H" or the number of hours (as the unit hours is indicated in the question). This can be determined with the formula <em>Distance = rate X time. </em>350 = 70 X H, in this case. To isolate the variable H, 70 (the rate) divides 350 (the total distance) into 5. 350 ÷ 70 = H. 5 = H, the amount of time spent traveling for 350 miles at a rate of 70 miles/hour.

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$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
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a)

so, if the population doubled in 5 years, that means t = 5. So say, if we use an amount for "i" or P in your case, to be 1, then after 5 years it'd be 2, and thus i = 1 and A = 2, let's find "r" or "k" in your equation.

$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &2\\
I=\textit{initial amount}\to &1\\
r=rate\\
t=\textit{elapsed time}\to &5\\
\end{cases}
\\\\\\
2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r
\\\\\\
\boxed{\cfrac{ln(2)}{5}=r}\qquad therefore\qquad \boxed{A=e^{\frac{ln(2)}{5}\cdot t}} \\\\\\
\textit{how long to tripling?}\quad 
\begin{cases}
A=3\\
I=1
\end{cases}\implies 3=1\cdot e^{\frac{ln(2)}{5}\cdot t}$

$\bf 3=e^{\frac{ln(2)}{5}\cdot t}\implies ln(3)=ln\left( e^{\frac{ln(2)}{5}\cdot t} \right)\implies ln(3)=\cfrac{ln(2)}{5} t
\\\\\\
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b)

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t=3
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\\\\\\
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