Question

a transit company operates commuter trains to help people get to the city each day. each train travels on a straight route to and from the farthest station, stopping at other stations along the route.
the graph shows the distance y miles the train is from the station after x minutes.
commuter train distance
based on the graph, what was the average speed, in miles per minute, of the train during the interval of 30 to 40 minutes?

Explanation:

Step1: Find the distance change

At \(x = 30\) minutes, \(y=0\) miles. At \(x = 40\) minutes, \(y = 15\) miles. The change in distance \(\Delta y=15 - 0=15\) miles.

Step2: Find the time change

The change in time \(\Delta x=40 - 30 = 10\) minutes.

Step3: Calculate the average speed

The formula for average speed \(v=\frac{\Delta y}{\Delta x}\). Substitute \(\Delta y = 15\) and \(\Delta x=10\) into the formula: \(v=\frac{15}{10}=1.5\) miles per minute.

Answer:

\(1.5\)