Math Problem Statement

The user provided a table with missing values in the 'Miles' and 'Hours' rows, asking for the missing values to be filled based on a constant rate of travel.

Solution

The image you've uploaded shows a table where "Miles" and "Hours" are given in two rows. There are some missing values in the table. Let's analyze and calculate the missing values.

The given data is:

\hline \text{Miles} & 0.6 & \_ & 1.8 & \_ \\ \hline \text{Hours} & 1 & 2 & \_ & 4 \\ \hline \end{array}$$ ### Step-by-Step Solution: This appears to involve a uniform rate of travel, where we can use the relation: $$\text{Rate} = \frac{\text{Miles}}{\text{Hours}}$$ Let’s assume the rate (speed) remains constant. First, calculate the rate using the data from the first column: $$\text{Rate} = \frac{0.6 \text{ miles}}{1 \text{ hour}} = 0.6 \text{ miles per hour}$$ Now, we can use this rate to fill in the missing values: 1. For the second column (Miles when Hours = 2): $$\text{Miles} = \text{Rate} \times \text{Hours} = 0.6 \times 2 = 1.2 \text{ miles}$$ 2. For the third column (Hours when Miles = 1.8): $$\text{Hours} = \frac{\text{Miles}}{\text{Rate}} = \frac{1.8}{0.6} = 3 \text{ hours}$$ 3. For the fourth column (Miles when Hours = 4): $$\text{Miles} = \text{Rate} \times \text{Hours} = 0.6 \times 4 = 2.4 \text{ miles}$$ ### Completed Table: $$\begin{array}{|c|c|c|c|c|} \hline \text{Miles} & 0.6 & 1.2 & 1.8 & 2.4 \\ \hline \text{Hours} & 1 & 2 & 3 & 4 \\ \hline \end{array}$$ Would you like further explanation or have any questions? Here are five related questions you might consider: 1. What formula relates distance, rate, and time in general motion problems? 2. How would the values change if the rate was doubled? 3. How can we calculate average speed if the rate is not constant? 4. How would you solve the problem if some values were missing in a non-linear relationship? 5. What real-world scenarios use the relation between miles, time, and speed? **Tip:** When solving rate problems, it's essential to ensure consistency in units (e.g., hours and miles) to avoid calculation errors.

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Math Problem Analysis

Mathematical Concepts

Proportions
Rates
Distance-Time Relationship

Formulas

Rate = Miles / Hours
Miles = Rate * Hours
Hours = Miles / Rate

Theorems

Constant Rate of Travel

Suitable Grade Level

Grades 6-8