Questions: A train travels approximately 400 miles, from San Francisco to Los Angeles, at an average of 50 miles per hour. Which graph shows the approximate distance between the train and Los Angeles as a function of time?

Solution Steps

The graph shows the distance from Los Angeles (L.A.) on the y-axis and time on the x-axis. The train is traveling from San Francisco to L.A. At the start, the train is approximately 400 miles away from L.A. As time progresses, the distance to L.A. decreases.

The train travels at an average speed of 50 miles per hour. This means that for every hour that passes, the distance to L.A. decreases by 50 miles.

The graph shows a linear relationship between distance and time. The distance decreases as time increases. The line starts at approximately 400 miles at time \(t = 0\) and appears to reach close to 0 miles around \(t = 50\) hours (though the time axis doesn't quite go that far). This is not consistent with the problem's information. Let's calculate what the graph should look like.

The total distance is 400 miles, and the speed is 50 miles per hour. The time taken to travel this distance can be calculated as: Time = Distance / Speed Time = 400 miles / 50 miles/hour Time = 8 hours

After 8 hours at a speed of 50 mph, the train would have traveled 400 miles. The distance between the train and L.A. decreases at a rate of 50 miles per hour. Therefore the graph should start at 400 miles and reach 0 after 8 hours. The given graph incorrectly represents this relationship, as it takes nearly 50 hours for the distance to reach 0 miles. The given graph represents a speed of roughly 400 miles/50 hours which is approximately 8 mph.

Final Answer