Question

By law, a bus driver may drive a maximum of 9 hours per day. If the speed limit is 65 miles per hour and if a driver needs to cover 4,287 miles, then what is the minimum number of days in which the driver can make the trip? A. 7 B. 8 C. 25 D. 66

Short answer

The minimum number of days the driver needs to complete the trip is 8. So, the correct answer is B. 8.

Step-by-step solution

Calculate the total hours needed to complete the trip

First, we need to determine how many hours the driver would need to cover all 4,287 miles if they were driving at 65 miles per hour. We can use the formula: Total hours needed = Total miles / Speed limit Total hours needed = \(4,287 / 65\)

Solve for the total hours needed

Divide 4,287 by 65 to find the total hours needed to complete the trip: Total hours needed ≈ 66.03 (round up to 67, since the driver needs extra time to complete the trip)

Calculate the minimum number of days needed

Now that we know the total hours needed to complete the trip, we will determine the minimum number of days the driver needs, given that they are allowed to drive for a maximum of 9 hours per day. To do this, we will divide the total hours needed by the number of hours they can drive per day: Minimum number of days = Total hours needed / Maximum hours per day Minimum number of days = \(67 / 9\)

Solve for the minimum number of days

Divide 67 by 9 to find the minimum number of days needed to complete the trip: Minimum number of days ≈ 7.44 (round up to 8, since the driver needs extra days to complete the trip) The minimum number of days the driver needs to complete the trip is 8. So, the correct answer is B. 8.

Key concepts

Math Word Problems

Solving math word problems is a critical skill not only in school but also in everyday life, especially for those preparing to take their General Educational Development (GED) test. A math word problem requires you to read, analyze, and then solve a situation that is presented in a narrative form. To solve these problems efficiently, one must understand the context and convert the verbal description into a mathematical equation.

For instance, with the exercise given about the bus driver, the problem presents a real-world scenario where a maximum driving time per day is set, and a total distance that needs to be covered. To tackle such problems, identifying the known quantities like the daily driving limit (9 hours), the speed (65 miles per hour), and the total distance (4,287 miles) is the first step. The challenge lies in translating this scenario into a mathematical model—in this case, a division problem to find out the total number of days required to complete the trip.

Useful tips for solving math word problems include:

• Reading the problem carefully and more than once if necessary.
• Identifying and noting down the key information.
• Determining what the problem is asking you to solve.
• Assigning variables to unknown quantities if needed.
• Setting up an equation based on the relationships between the quantities.
• Solving the equation step by step.
• Checking your answer to ensure it makes sense with the problem.

Rate and Time Calculations

Rate and time calculations are essential components of many mathematical problems, including those on the GED test. A rate is a ratio that compares two different kinds of measurements, like miles per hour in the context of speed.

In the given exercise, we are dealing with the concept of speed – which is a type of rate where distance is covered over time. The formula for calculating the time needed based on distance and rate is given by Time = Distance / Rate. To calculate the minimum number of days a bus driver needs to complete a trip, you must first determine the total time required by using the speed limit and total miles.

Considerations When Calculating Rate and Time

• Ensure all units are consistent before calculating. For example, if speed is in miles per hour, then distance should also be in miles, and time in hours.
• Understand that time cannot be negative, and in practical scenarios like driving, it often needs to be rounded up to account for partial hours.
• Remember to consider maximum or minimum constraints, such as the legal driving hours in this scenario.

Once you have the total time, you'll need to divide it by the maximum rate—or in this case, the maximum number of hours the bus driver can legally drive per day (9 hours), to find out how many days the trip will take.

GED Test Preparation

Preparing for the GED test can be a daunting task, but with the right resources and study habits, it is a goal that can be achieved. The GED test covers four main content areas: Mathematical Reasoning, Reasoning Through Language Arts, Science, and Social Studies. A strong foundation in math is crucial, as the Mathematical Reasoning section not only tests basic arithmetic but also algebra, geometry, and data analysis.

To prepare effectively for the GED, particularly the math segment, it’s important to:

• Study and review core math concepts regularly.
• Work on practice problems, like the rate and time calculation exercise provided, which can help you become familiar with the types of questions that will be on the test.
• Take timed practice tests to improve speed and accuracy under exam conditions.
• Analyze and understand your mistakes in practice problems to avoid making the same errors on the actual test.
• Use study guides and educational platforms that break down problems step by step to aid in comprehension.

Remember, the key to success on the GED test is not just memorization but understanding how to apply mathematical principles to solve real-world problems.