Solve each problem. If a train travels at 80 mph for 15 min, what is the distance traveled?

Verified step by step guidance

1. Identify the given values: speed \(v = 80\) mph and time \(t = 15\) minutes.
2. Convert the time from minutes to hours because the speed is in miles per hour. Since 1 hour = 60 minutes, calculate \(t\) in hours as \(t = \frac{15}{60}\) hours.
3. Recall the formula for distance traveled: \(d = v \times t\), where \(d\) is distance, \(v\) is speed, and \(t\) is time.
4. Substitute the known values into the formula: \(d = 80 \times \frac{15}{60}\).
5. Simplify the expression to find the distance traveled in miles.

Key Concepts

Speed-Distance-Time Relationship

This fundamental formula relates speed, distance, and time through the equation distance = speed × time. Understanding this relationship allows you to calculate one quantity if the other two are known, which is essential for solving motion problems.

Unit Conversion

Converting units correctly is crucial, especially when time is given in minutes and speed in miles per hour. You must convert time into hours to match the speed units before applying the formula to ensure accurate calculations.

Multiplying Fractions and Decimals

When calculating distance, you often multiply speed by a fractional time value (e.g., 15 minutes as 0.25 hours). Being comfortable with multiplying decimals or fractions helps in performing these calculations accurately.