Q71. - Algebra 2

Question

For exercises 71-73, use the following information.

The First Transcontinental Railroad was built by two companies. The Central Pacific began building eastward from Sacramento, California, while the Union Pacific built westwards from Omaha, Nebraska. The two lines met at Promontory, Utah, in 1869, about 6 years after construction began.

71. The Central Pacific Company laid an average of $\mathbf{9}\mathbf{.}\mathbf{6}$ miles of track per month. Together the two companies laid a total of 1775 miles of track. Determine the average number of miles of track laid per month by the Union Pacific company.  

Step-by-Step Solution

Answer

The average number of miles of track laid per month by the Union Pacific Company is $\mathbf{15}\mathbf{.}\mathbf{0527778}$.

Step 1 ­- Description of step.

It is given that the construction was completed in 6 years.

It is known that 1 year=12 months.

Therefore, it can be obtained that:

$\begin{array}{c}\text{6 years = 6×12 months}\\ \text{= 72 months}\end{array}$

Step 2 ­- Description of step.

It is given that the Central Pacific Company laid an average of $9.6$ miles of track per month.

That implies in 1 month it laid $9.6$ miles of track.

Therefore, in 72 months it will lay:

$9.6\times 72=691.2$

Therefore, in 72 months it will lay $691.2$ miles of track.

It is given that the total of 1775 miles of track has been laid.

Therefore, the sum of the miles of track laid by Central Pacific Company and Union Pacific Company is 1775.

Therefore, it can be obtained that:

$\begin{array}{c}\text{691.2+miles of track laid by Union Pacific company=1775}\\ \text{miles of track laid by Union Pacific company}+691.2-691.2=1755-691.2\\ \text{miles of track laid by Union Pacific company}=1083.8\end{array}$

Therefore, the miles of track laid by Union Pacific Company is $1083.8$ miles

Step 3 ­- Description of step.

Calculate the average number of miles of track laid per month by the Union Pacific Company by dividing the miles of track laid by Union Pacific Company by 72.

Therefore, it can be obtained that:

$\begin{array}{c}\text{average number of miles of track laid per month by the Union Pacific Company=}\frac{\text{1083.8}}{\text{72}}\\ \text{=15.0527778}\end{array}$

Therefore, the average number of miles of track laid per month by the Union Pacific Company is $15.0527778$