Question

Traveling at an average speed of 58 miles per hour, Terence drives 145 miles. Three hours later, Terence makes the return trip at the same speed. How much total time elapses between Terence's original departure and final return? A. 2.5 hours B. 5 hours C. 5.5 hours D. 8 hours

Short answer

The total time elapsed between Terence's original departure and final return is 8 hours. Answer: $\boxed{{\displaystyle \text{D. 8 hours}}}$.

Step-by-step solution

1. Find the time it takes to travel 145 miles at 58 mph

To find the time it takes for Terence to travel 145 miles at 58 mph, we can use the distance formula: distance = speed × time 145 miles = 58 mph × t Now, we need to solve for t: t = 145 miles / 58 mph

2. Calculate t

Now we can calculate t by dividing 145 by 58: t = 145/58 = 2.5 hours So, it takes Terence 2.5 hours to travel 145 miles at an average speed of 58 mph.

3. Calculate time for the return trip

Since the return trip is at the same speed, it will also take Terence 2.5 hours to travel back.

4. Add time for the stop

Terence stops for 3 hours before making the return trip. So, we need to add those 3 hours to the total time elapsed.

5.Calculate total time elapsed

Now, we can calculate the total time elapsed by adding the times for each leg of the trip and the time for Terence's stop: Total time elapsed = 2.5 hours (original trip) + 3 hours (stop) + 2.5 hours (return trip) Total time elapsed = 8 hours So, the total time elapsed between Terence's original departure and final return is 8 hours. The correct answer is D. 8 hours.

Key concepts

Distance Speed Time Problems

Understanding distance, speed, and time relationships is a fundamental concept in mathematics, especially when it comes to preparing for exams like the GED. The basic formula connecting these three quantities is expressed as:

$$\text{Distance}=\text{Speed}\times \text{Time}$$

This equation can be rearranged to solve for any one of the three variables, given the other two. Let's say you're given the speed and distance, like in Terence's problem, you can find the time by rearranging the formula to $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$.

Considerations for Distance Speed Time Calculations

• Units: Ensure that the units for speed and time are compatible. If speed is in miles per hour and distance in miles, time must be calculated in hours.
• Consistent Speed: The formula assumes a constant speed throughout the journey. Any changes in speed would require additional calculations.
• Multiple Legs: When a trip has several parts, calculate each part separately and sum them for the total time. In the GED math practice scenario with Terence, the trip had two legs plus a stop.

Remember that knowing how to manipulate this formula is crucial for solving distance, speed, and time problems effectively.

GED Algebra Problems

Algebra is a significant component of the GED math test, and it requires students to be comfortable with using letters to represent numbers in equations and inequalities. One common type of problem involves solving for an unknown, which can be approached using algebraic manipulation.

For example, when determining the time it takes for Terence to travel a certain distance, we start with the algebraic expression $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$. Solving this provides us with a specific value for the time variable. This step is critical in GED algebra problems as it demonstrates the ability to manipulate and solve equations.

Key Algebra Concepts

• Variables: Variables represent unknown values and are central to algebraic equations.
• Solving Equations: The process of finding the value of the variable that makes the equation true.
• Equation Balancing: Whatever operation is done to one side of the equation should be done to the other to maintain balance.

Strengthening these algebra skills is crucial for success in GED math and beyond.

GED Test Preparation

Proper preparation for the GED test is essential to succeed, and for the math section, this involves a solid understanding of a range of mathematical concepts, including algebra, geometry, data analysis, and arithmetic operations.

When preparing for the math section, practice a variety of problems to become comfortable with different types of questions. Use practice tests to identify areas of strength and weakness. Focus on improving weak areas while also reinforcing stronger skills.

Effective Study Strategies for the GED Math Test

• Understand the Concepts: Don’t just memorize procedures; aim to understand the underlying concepts.
• Practice Regularly: Consistency in practice helps to reinforce learning and improve retention.
• Simulate Testing Conditions: Taking timed practice tests can help you manage time during the actual exam.

Remember, resourcefulness is as important as memory and practice. Familiarize yourself with the types of math tools allowed, such as calculators, and how to use them effectively during the test.