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.Ask a new question for Free
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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
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