Problem 42 - Elementary Algebra

Question

\(\frac{55 \mathrm{mi}}{1 \mathrm{hr}} ; 7 \mathrm{hr}\)

Step-by-Step Solution

Answer

385 miles

Step 1 - Identify the information given

The problem provides the speed: \( 55 \mathrm{mi/hr} \) and the time: \( 7 \mathrm{hr} \).

Step 2 - Write the formula for distance

Use the formula \( \text{Distance} = \text{Speed} \times \text{Time} \)

Step 3 - Substitute the values into the formula

Substitute the given values into the formula: \[ \text{Distance} = 55 \mathrm{mi/hr} \times 7 \mathrm{hr} \]

Step 4 - Perform the multiplication

Multiply the speed and time: \[ 55 \mathrm{mi/hr} \times 7 \mathrm{hr} = 385 \mathrm{mi} \]

Step 5 - State the final answer

Thus, the total distance traveled in 7 hours at a speed of 55 miles per hour is 385 miles.

Key Concepts

speed and time relationship

Understanding how speed and time relate to each other is crucial in solving many distance problems. Speed tells you how fast you are moving, usually measured in units like miles per hour (mi/hr) or kilometers per hour (km/hr).
Time tells you how long you have been moving, typically measured in hours, minutes, or seconds. When you know both speed and time, you can calculate the distance traveled.
Imagine driving a car: if you know you are traveling at 55 miles per hour and you drive for 7 hours, you can calculate the distance by understanding the relationship between speed and time.

multiplication

Multiplication is a key operation in many math problems, including distance calculations. In this context, you're often multiplying two values: speed and time. This operation helps you find out how far you have traveled.
In our example, the speed is 55 miles per hour and the time is 7 hours. To find the distance, multiply these two numbers: \[ \text{Distance} = 55 \text{ mi/hr} \times 7 \text{ hr} \]
This operation is straightforward and shows how useful multiplication is in everyday calculations.

• Speed: 55 mi/hr
• Time: 7 hr

Performing the multiplication, you get \[ 55 \text{ mi/hr} \times 7 \text{ hr} = 385 \text{ mi} \]

distance formula

The formula for calculating distance is a fundamental concept that brings together speed and time.
The distance formula is: \[ \text{Distance} = \text{Speed} \times \text{Time} \]
This formula is very useful and can be applied in many real-life situations. To use it, you need to know the speed and the time, and simply multiply these two values.
In the given example, the speed provided is 55 mi/hr and the time is 7 hr. Plugging these values into the formula, we get: \[ \text{Distance} = 55 \text{ mi/hr} \times 7 \text{ hr} = 385 \text{ mi} \]
This tells you that traveling at a speed of 55 miles per hour for 7 hours will cover a distance of 385 miles. Using this formula makes distance calculations clear and straightforward.