Question

A train and car leave from the Pasadena railroad station at the same time headed for the state fair in Sacramento. The car averages 50 miles per hour, and the train averages 70 miles per hour. If the train arrives at the fair 2 hours ahead of the car, find the distance from the railroad station to the state fair.

Answer 1

To find the distance from the Pasadena railroad station to the state fair, we need to calculate the time it takes for the car and the train to travel. By equating the expressions for time based on their average speeds, we can solve for the distance.

Step-by-step explanation:

To find the distance from the Pasadena railroad station to the state fair, we need to calculate the time it takes for the car and the train to travel. Let's assume the distance between the two is d.

Since the car travels at an average speed of 50 miles per hour, it will take t = d/50 hours to reach the fair.

Similarly, since the train travels at an average speed of 70 miles per hour, it will take t-2 = d/70 hours to reach the fair, arriving 2 hours earlier than the car.

Now, equating both expressions for t, we get: d/50 = d/70 + 2. Solving this equation will give us the value of d.