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Chapter 2: Problem 70

At an average speed of 125 mph, how long would a race car take to complete a 500 -mile race?

Short Answer

Expert verified
The race car will take 4 hours to complete the 500-mile race.

Step by step solution

01

- Recall the formula for time

To find the time taken, you can use the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
02

- Insert the given values into the formula

The distance of the race is given as 500 miles and the speed of the race car is 125 mph. Insert these values into the formula: \[ \text{Time} = \frac{500 \text{ miles}}{125 \text{ mph}} \]
03

- Calculate the time

Divide the distance by the speed: \[ \text{Time} = \frac{500}{125} = 4 \text{ hours} \]
04

- Conclude the result

It will take the race car 4 hours to complete the 500-mile race.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

distance
In the context of this exercise, the term 'distance' refers to how far the race car needs to travel to complete the race. Distance is a scalar quantity, meaning it only has magnitude and no direction. For the given problem, distance is mentioned as 500 miles. Whenever you're dealing with real-life problems like this, always ensure the distance is in consistent units, such as miles or kilometers, as this helps avoid confusion during calculations.
speed
Speed is how fast an object is moving, regardless of its direction. It's also a scalar quantity. The speed given in the exercise is 125 mph (miles per hour), which tells us how many miles the race car covers in one hour. Always make sure to use the same units for speed as the distance to keep calculations straightforward. Understanding speed is crucial because it helps you determine how long it will take to cover a certain distance, which leads us to our next concept.
time calculation
To find out how long it takes to cover a particular distance at a certain speed, you can use the formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\). In this example, we are given a distance of 500 miles and a speed of 125 mph. By inserting these values into the formula, we find the calculation is \[ \text{Time} = \frac{500 \text{ miles}}{125 \text{ mph}} = 4 \text{ hours} \]. This means it would take 4 hours to complete the race. Time calculation becomes straightforward when you remember to keep the units consistent and use the formula correctly.
formula application
Applying formulas is an essential step in solving such problems. The formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\) should be used in any situation involving constant speed and distance to find time. Here's a brief guide on how to apply this formula:

  • Identify the quantities you're given (distance and speed)
  • Ensure both are in compatible units
  • Plug the values into the formula
  • Perform the arithmetic operations
  • Interpret the result, which should be in time units like hours or minutes
By following these steps, you can solve distance-speed-time problems accurately and efficiently.

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Most popular questions from this chapter

A rubber ball is thrown straight up into the air with an initial speed of \(20 \mathrm{m} / \mathrm{s}\). If we do not neglect air resistance as the ball moves upward, is the acceleration of the ball greater than, equal to, or less than the acceleration due to gravity?

A motorcycle travels down a straight highway with uniform speed of 35 mph. A sports car starts from rest and accelerates at \(10 \mathrm{mph} / \mathrm{s}\). Which will be moving faster after 3 seconds?

Which of the following (if any) could not be considered an "accelerator" in an automobile-gas pedal, brake pedal, or steering wheel?

How did the ideas of Galileo and Aristotle differ concerning the motion of a freely falling object?

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