7.RP.1: Worksheet featuring ten math problems related to unit rates, ratios, and proportions, including scenarios like running speed, eating rates, and gas prices.

Let's solve each problem step-by-step from the 7.RP.1: Worksheet. These problems focus on unit rates, which are rates expressed as a quantity per one unit of another (e.g., miles per hour, burgers per minute).

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Problem 1:

Ayesha can run half a kilometer in $3\frac{1}{2}$ minutes. What's her unit rate?

- Half a kilometer = $ \frac{1}{2} $ km
- Time = $ 3\frac{1}{2} = \frac{7}{2} $ minutes

We want km per minute:
$$
\text{Rate} = \frac{\frac{1}{2}}{\frac{7}{2}} = \frac{1}{2} \times \frac{2}{7} = \frac{1}{7} \text{ km/min}
$$

But usually, we express speed in km/hour.

Convert to km/hour:
$$
\frac{1}{7} \text{ km/min} \times 60 \text{ min/hour} = \frac{60}{7} \approx 8.57 \text{ km/h}
$$

✔ Answer: $ \boxed{\frac{60}{7}} $ km/h or approximately 8.57 km/h

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Problem 2:

What’s an equivalent unit rate to eating 5 burgers in $ \frac{1}{3} $ of a minute?

- Burgers: 5
- Time: $ \frac{1}{3} $ minute

Rate = $ \frac{5}{\frac{1}{3}} = 5 \times 3 = 15 $ burgers per minute

✔ Answer: $ \boxed{15} $ burgers per minute

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Problem 3:

Teddy can watch $ \frac{4}{3} $ commercials in $ \frac{1}{6} $ of an hour. How many could he watch in an hour?

- Commercials: $ \frac{4}{3} $
- Time: $ \frac{1}{6} $ hour

Rate = $ \frac{\frac{4}{3}}{\frac{1}{6}} = \frac{4}{3} \times 6 = 8 $ commercials per hour

✔ Answer: $ \boxed{8} $ commercials per hour

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Problem 4:

A recipe calls for $ \frac{1}{2} $ cup of sugar and $ \frac{3}{4} $ cup of flour. If you’ve got 3 cups of flour and want to adjust the recipe so you use it all, how much sugar do you need?

Find the ratio of sugar to flour:
$$
\frac{\text{sugar}}{\text{flour}} = \frac{1/2}{3/4} = \frac{1}{2} \times \frac{4}{3} = \frac{2}{3}
$$

So for every 1 cup of flour, you need $ \frac{2}{3} $ cup of sugar.

For 3 cups of flour:
$$
3 \times \frac{2}{3} = 2 \text{ cups of sugar}
$$

✔ Answer: $ \boxed{2} $ cups of sugar

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Problem 5:

Josie can hit 8 different notes in half a second. How many notes can she play in a minute?

- In $ \frac{1}{2} $ second → 8 notes
- So in 1 second → $ 8 \times 2 = 16 $ notes
- In 60 seconds → $ 16 \times 60 = 960 $ notes

✔ Answer: $ \boxed{960} $ notes per minute

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Problem 6:

The track at Bronwyn’s school is $ \frac{1}{4} $ mile around. If she can do 3 laps in $ 4\frac{1}{2} $ minutes, how fast is she running in miles per hour?

- Distance per lap: $ \frac{1}{4} $ mile
- 3 laps = $ 3 \times \frac{1}{4} = \frac{3}{4} $ miles
- Time: $ 4\frac{1}{2} = \frac{9}{2} $ minutes

Speed in miles per minute:
$$
\frac{3/4}{9/2} = \frac{3}{4} \times \frac{2}{9} = \frac{6}{36} = \frac{1}{6} \text{ mi/min}
$$

Convert to mph:
$$
\frac{1}{6} \times 60 = 10 \text{ mph}
$$

✔ Answer: $ \boxed{10} $ miles per hour

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Problem 7:

If Emeril can grill $ \frac{6}{7} $ of a steak in $ \frac{3}{14} $ of an hour, how many steaks can he grill in a full hour?

- Steaks grilled: $ \frac{6}{7} $
- Time: $ \frac{3}{14} $ hours

Rate = $ \frac{6/7}{3/14} = \frac{6}{7} \times \frac{14}{3} = \frac{84}{21} = 4 $

So he grills 4 steaks per hour

✔ Answer: $ \boxed{4} $ steaks per hour

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Problem 8:

Jo paid $10.25 for $ \frac{5}{2} $ gallons of gas. What is the price per gallon?

- Total cost: $10.25
- Gallons: $ \frac{5}{2} = 2.5 $

Price per gallon:
$$
\frac{10.25}{2.5} = 4.10
$$

✔ Answer: $ \boxed{\$4.10} $ per gallon

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Problem 9:

A Boeing 747 cruises at 570 mph. How far can it fly in $ \frac{9}{8} $ hours?

Use: Distance = Rate × Time
$$
570 \times \frac{9}{8} = \frac{5130}{8} = 641.25 \text{ miles}
$$

✔ Answer: $ \boxed{641.25} $ miles

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Problem 10:

You finished all 10 problems in $ 6\frac{2}{3} $ minutes. What was your unit rate?

- Problems: 10
- Time: $ 6\frac{2}{3} = \frac{20}{3} $ minutes

Unit rate = problems per minute:
$$
\frac{10}{20/3} = 10 \times \frac{3}{20} = \frac{30}{20} = \frac{3}{2} = 1.5 \text{ problems per minute}
$$

Alternatively, problems per minute: $ \boxed{1.5} $

✔ Answer: $ \boxed{1.5} $ problems per minute

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{60}{7} $ km/h ≈ 8.57 km/h |
| 2 | 15 burgers per minute |
| 3 | 8 commercials per hour |
| 4 | 2 cups of sugar |
| 5 | 960 notes per minute |
| 6 | 10 mph |
| 7 | 4 steaks per hour |
| 8 | \$4.10 per gallon |
| 9 | 641.25 miles |
| 10 | 1.5 problems per minute |

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