Unit Rate Problems 6th Grade - Free Printable

The image you provided is a worksheet titled "UNIT RATES IN TABLES SHEET 4.2." The task involves calculating unit rates for various scenarios based on the given data. Below, I will solve each problem step by step and explain the solution.

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Problem 1: Hedgehog

- Given Data:
- Distance (miles): 36
- Time (hours): 4

- Task: Find the unit rate in miles per hour.

#### Solution:
To find the unit rate (miles per hour), divide the total distance by the total time:
\[
\text{Unit Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{36 \text{ miles}}{4 \text{ hours}} = 9 \text{ miles per hour}
\]

- Answer: 9 miles per hour

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Problem 2: Bicycle

- Given Data:
- Distance (miles): 35
- Time (hours): 7

- Task: Find the unit rate in miles per hour.

#### Solution:
To find the unit rate (miles per hour), divide the total distance by the total time:
\[
\text{Unit Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{35 \text{ miles}}{7 \text{ hours}} = 5 \text{ miles per hour}
\]

- Answer: 5 miles per hour

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Problem 3: Motorcycle

- Given Data:
- Distance (miles): 180
- Time (hours): 3

- Task: Find the unit rate in miles per hour.

#### Solution:
To find the unit rate (miles per hour), divide the total distance by the total time:
\[
\text{Unit Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{180 \text{ miles}}{3 \text{ hours}} = 60 \text{ miles per hour}
\]

- Answer: 60 miles per hour

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Problem 4: Number of Articles

- Given Data:
- Number of Articles: 275
- Time (minutes): 5

- Task: Find the unit rate in articles per minute.

#### Solution:
To find the unit rate (articles per minute), divide the total number of articles by the total time:
\[
\text{Unit Rate} = \frac{\text{Number of Articles}}{\text{Time}} = \frac{275 \text{ articles}}{5 \text{ minutes}} = 55 \text{ articles per minute}
\]

- Answer: 55 articles per minute

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Problem 5: Pages Read

- Given Data:
- Pages read: 112
- Time (hours): 2

- Task: Find the unit rate in pages per hour.

#### Solution:
To find the unit rate (pages per hour), divide the total number of pages by the total time:
\[
\text{Unit Rate} = \frac{\text{Pages read}}{\text{Time}} = \frac{112 \text{ pages}}{2 \text{ hours}} = 56 \text{ pages per hour}
\]

- Answer: 56 pages per hour

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Problem 6: Gallons of Milk

- Given Data:
- Gallons of milk: 165
- Cost (\$): 55

- Task: Find the unit rate in dollars per gallon.

#### Solution:
To find the unit rate (dollars per gallon), divide the total cost by the total gallons:
\[
\text{Unit Rate} = \frac{\text{Cost}}{\text{Gallons}} = \frac{55 \text{ dollars}}{165 \text{ gallons}} = \frac{1}{3} \text{ dollars per gallon}
\]

- Answer: $\frac{1}{3}$ dollars per gallon

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Problem 7: Pencils

- Given Data:
- Pencils: 0
- Cost (\$): 0

- Task: Find the unit rate in dollars per pencil.

#### Solution:
Since both the number of pencils and the cost are zero, the unit rate is undefined because division by zero is not possible.

- Answer: Undefined

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Problem 8: Bottled Water

- Given Data:
- Bottles of water: 2
- Cost (\$): 2

- Task: Find the unit rate in dollars per bottle.

#### Solution:
To find the unit rate (dollars per bottle), divide the total cost by the total number of bottles:
\[
\text{Unit Rate} = \frac{\text{Cost}}{\text{Bottles}} = \frac{2 \text{ dollars}}{2 \text{ bottles}} = 1 \text{ dollar per bottle}
\]

- Answer: 1 dollar per bottle

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Final Answers:

1. Hedgehog: 9 miles per hour
2. Bicycle: 5 miles per hour
3. Motorcycle: 60 miles per hour
4. Number of Articles: 55 articles per minute
5. Pages Read: 56 pages per hour
6. Gallons of Milk: $\frac{1}{3}$ dollars per gallon
7. Pencils: Undefined
8. Bottled Water: 1 dollar per bottle

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Boxed Final Answer:

\[
\boxed{9, 5, 60, 55, 56, \frac{1}{3}, \text{Undefined}, 1}
\]