Question

Two freight trains are delivering cargo. One freight train is delivering coal, and the other freight train is delivering grain. Their respective distances traveled after x hours is represented in the table and graph below.

Answer 1

- In order to find which of the trains is moving faster, we should calculate the average speeds of both trains and compare them.

- The y-values of both trains are the Distance in Miles and the x-axis is the time in hours.

- Thus, the best way to calculate their average speeds is to find the slope of both datasets.

- The formula for calculating the slope is given below:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \text{where,} \\ (x_1,y_1)\text{ and (}x_2,y_2)\text{ are coordinates chosen} \end{gathered}`

- Thus, with the above information, we can proceed to solve the question

Speed of Coal Freight Train:

`\begin{gathered} \text{ Choosing } \\ (x_1,y_1)=(1,49) \\ (x_2,y_2)=(2,98) \\ \\ m_C=(y_2-y_1)/(x_2-x_1)=(98-49)/(2-1) \\ \\ \therefore m_C=49\text{miles per hour} \end{gathered}`

Speed of Grain Freight Train:

`\begin{gathered} \text{Reading off the graph that passes through the origin, we choose:} \\ (0,0)\text{ and }(1,45) \\ \\ \therefore m_G=(45-0)/(1-0)=45 \\ \\ m_G=45\text{miles per hour} \end{gathered}`

- From the above calculations, we can easily observe that the Speed of the Coal Freight Train is greater than the speed of the Grain Freight Train

Final Answer

"The Coal Freight Train is traveling at a faster speed" (OPTION 2)