This worksheet helps students practice converting complex unit rates, such as changing kilometers per hour into meters per second.

Problem: Converting Rates Worksheet

The task involves converting given rates into different units using the desired units of measurement. Below, I will solve each problem step by step and explain the solution.

---

#### 1. Convert 55 km / hour into m / minute

Given:
55 km / hour

Desired Units:
m / minute

Solution Steps:
1. Convert kilometers to meters:
1 km = 1000 meters.
So, 55 km = \( 55 \times 1000 = 55,000 \) meters.

2. Convert hours to minutes:
1 hour = 60 minutes.

3. Calculate the rate in meters per minute:
\[
\text{Rate} = \frac{55,000 \text{ meters}}{60 \text{ minutes}}
\]
Simplify:
\[
\text{Rate} = \frac{55,000}{60} = 916.67 \text{ meters per minute}
\]

Final Answer:
\[
\boxed{916.67 \text{ m/minute}}
\]

---

#### 2. Convert 5 feet / minute into feet / second

Given:
5 feet / minute

Desired Units:
feet / second

Solution Steps:
1. Convert minutes to seconds:
1 minute = 60 seconds.

2. Calculate the rate in feet per second:
\[
\text{Rate} = \frac{5 \text{ feet}}{60 \text{ seconds}}
\]
Simplify:
\[
\text{Rate} = \frac{5}{60} = 0.0833 \text{ feet per second}
\]

Final Answer:
\[
\boxed{0.0833 \text{ feet/second}}
\]

---

#### 3. Convert 2 liters / km into liters / meter

Given:
2 liters / km

Desired Units:
liters / meter

Solution Steps:
1. Convert kilometers to meters:
1 km = 1000 meters.

2. Calculate the rate in liters per meter:
\[
\text{Rate} = \frac{2 \text{ liters}}{1000 \text{ meters}}
\]
Simplify:
\[
\text{Rate} = \frac{2}{1000} = 0.002 \text{ liters per meter}
\]

Final Answer:
\[
\boxed{0.002 \text{ liters/meter}}
\]

---

#### 4. Convert $1.50 / kg into $ / gram

Given:
$1.50 / kg

Desired Units:
$ / gram

Solution Steps:
1. Convert kilograms to grams:
1 kg = 1000 grams.

2. Calculate the rate in dollars per gram:
\[
\text{Rate} = \frac{1.50 \text{ dollars}}{1000 \text{ grams}}
\]
Simplify:
\[
\text{Rate} = \frac{1.50}{1000} = 0.0015 \text{ dollars per gram}
\]

Final Answer:
\[
\boxed{0.0015 \text{ dollars/gram}}
\]

---

#### 5. Convert $100 / day into $ / 5-hour

Given:
$100 / day

Desired Units:
$ / 5-hour

Solution Steps:
1. Convert days to hours:
1 day = 24 hours.

2. Calculate the rate in dollars per hour:
\[
\text{Rate per hour} = \frac{100 \text{ dollars}}{24 \text{ hours}}
\]
Simplify:
\[
\text{Rate per hour} = \frac{100}{24} \approx 4.17 \text{ dollars per hour}
\]

3. Calculate the rate for 5 hours:
\[
\text{Rate for 5 hours} = 4.17 \times 5 = 20.83 \text{ dollars per 5 hours}
\]

Final Answer:
\[
\boxed{20.83 \text{ dollars/5-hour}}
\]

---

#### 6. Convert 3,000 nanometers / second into meters / minute

Given:
3,000 nanometers / second

Desired Units:
meters / minute

Solution Steps:
1. Convert nanometers to meters:
1 nanometer = \(10^{-9}\) meters.
So, 3,000 nanometers = \(3,000 \times 10^{-9} = 3 \times 10^{-6}\) meters.

2. Convert seconds to minutes:
1 minute = 60 seconds.

3. Calculate the rate in meters per minute:
\[
\text{Rate} = \frac{3 \times 10^{-6} \text{ meters}}{1 \text{ second}} \times 60 \text{ seconds per minute}
\]
Simplify:
\[
\text{Rate} = (3 \times 10^{-6}) \times 60 = 1.8 \times 10^{-4} \text{ meters per minute}
\]

Final Answer:
\[
\boxed{1.8 \times 10^{-4} \text{ meters/minute}}
\]

---

#### 7. Convert 2.50 / gram into ounces / gram

Given:
2.50 / gram

Desired Units:
ounces / gram

Solution Steps:
- The problem seems incomplete or unclear because "2.50" is not specified as a unit (e.g., dollars, pounds, etc.). Assuming it is a weight-related conversion, we need more context. If you can clarify, I can provide a precise solution.

---

#### 8. Convert 20 grains / liter into grams / milliliter

Given:
20 grains / liter

Desired Units:
grams / milliliter

Solution Steps:
1. Convert grains to grams:
1 grain ≈ 0.0647989 grams.
So, 20 grains = \( 20 \times 0.0647989 = 1.295978 \) grams.

2. Convert liters to milliliters:
1 liter = 1000 milliliters.

3. Calculate the rate in grams per milliliter:
\[
\text{Rate} = \frac{1.295978 \text{ grams}}{1000 \text{ milliliters}}
\]
Simplify:
\[
\text{Rate} = \frac{1.295978}{1000} = 0.001296 \text{ grams per milliliter}
\]

Final Answer:
\[
\boxed{0.001296 \text{ grams/milliliter}}
\]

---

#### 9. Convert 5.1 / kg into quarters / kg

Given:
5.1 / kg

Desired Units:
quarters / kg

Solution Steps:
- The problem is incomplete because "5.1" is not specified as a unit (e.g., dollars, pounds, etc.). Assuming it is a weight-related conversion, we need more context. If you can clarify, I can provide a precise solution.

---

#### 10. Convert $2 / liter into nickels / liter

Given:
$2 / liter

Desired Units:
nickels / liter

Solution Steps:
1. Convert dollars to nickels:
1 dollar = 20 nickels.
So, $2 = \( 2 \times 20 = 40 \) nickels.

2. Calculate the rate in nickels per liter:
\[
\text{Rate} = 40 \text{ nickels per liter}
\]

Final Answer:
\[
\boxed{40 \text{ nickels/liter}}
\]

---

#### 11. Convert 4 km / hour into m / second

Given:
4 km / hour

Desired Units:
m / second

Solution Steps:
1. Convert kilometers to meters:
1 km = 1000 meters.
So, 4 km = \( 4 \times 1000 = 4000 \) meters.

2. Convert hours to seconds:
1 hour = 3600 seconds.

3. Calculate the rate in meters per second:
\[
\text{Rate} = \frac{4000 \text{ meters}}{3600 \text{ seconds}}
\]
Simplify:
\[
\text{Rate} = \frac{4000}{3600} \approx 1.11 \text{ meters per second}
\]

Final Answer:
\[
\boxed{1.11 \text{ m/second}}
\]

---

Final Answers Summary:

1. \(\boxed{916.67 \text{ m/minute}}\)
2. \(\boxed{0.0833 \text{ feet/second}}\)
3. \(\boxed{0.002 \text{ liters/meter}}\)
4. \(\boxed{0.0015 \text{ dollars/gram}}\)
5. \(\boxed{20.83 \text{ dollars/5-hour}}\)
6. \(\boxed{1.8 \times 10^{-4} \text{ meters/minute}}\)
7. Needs clarification.
8. \(\boxed{0.001296 \text{ grams/milliliter}}\)
9. Needs clarification.
10. \(\boxed{40 \text{ nickels/liter}}\)
11. \(\boxed{1.11 \text{ m/second}}\)