Solve each problem. How long will it take a car to travel 400 mi at an average rate of 50 mph?

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Identify the formula relating distance, rate, and time: \(\text{Distance} = \text{Rate} \times \text{Time}\).

Rearrange the formula to solve for time: \(\text{Time} = \frac{\text{Distance}}{\text{Rate}}\).

Substitute the given values into the formula: \(\text{Time} = \frac{400}{50}\).

Simplify the fraction to find the time it takes to travel 400 miles at 50 mph.

Interpret the result as the number of hours required for the trip.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Distance, Rate, and Time Relationship

This concept involves the fundamental formula relating distance, rate (speed), and time: Distance = Rate × Time. Understanding this relationship allows you to solve for any one of the variables if the other two are known, which is essential for problems involving motion.

Solving for Time

To find the time taken for a trip, rearrange the formula to Time = Distance ÷ Rate. This step is crucial because the question asks for the duration of travel, requiring you to isolate and calculate the time variable using the given distance and speed.

Units and Unit Consistency

Ensuring that units are consistent is vital for accurate calculations. Here, distance is in miles and rate is in miles per hour, so the resulting time will be in hours. Recognizing and maintaining consistent units prevents errors in interpreting the answer.

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