Answer:
1986
Step-by-step explanation:
Function that represents railroad miles
[tex]y=-1250.2x + 142602[/tex]
Function that represents number of highway miles
[tex]y=501.5x + 158449[/tex]
We have to find in which year (1995+x) the miles of railroad and highway is the same so
[tex]-1250.2x + 142602=501.5x + 158449\\\Rightarrow -1250.2x-501.5x=158449-142606\\\Rightarrow -1751.7x=15843\\\Rightarrow x=-\dfrac{15843}{1751.7}\\\Rightarrow x=-9.044\ \text{years}\approx -9\ \text{years}[/tex]
So, the year is [tex]1995+x=1995+(-9)=1986[/tex]
In the year 1986 the railroad and highway miles were equal.
It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
Given
The function y =-1250.2x + 142,602 represents the railrond miles.
While the function y =501.5x + 158,449 models the number of highway miles.
For each function, x is the number of years after 1995.
The year in which it is estimated that the number of the country's railroad miles and the number of the country's highway miles were the same.
Therefore,
[tex]\rm -1250.2x + 142,602=501.5x + 158,449\\\\-1250.2x -501.5x = 158,449-142,602\\\\-1751.7x=15847\\\\x = \dfrac{15847}{-1751.7}\\\\x=-9[/tex]
Then,
1995 - 9 = 1986
It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
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