Unit Rates

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Unit Rates · Grade 6 · Worksheet 1

1. Emma is training for a marathon and tracks her running pace. She runs 8 kilometers in 48 minutes. What is Emma's running speed in kilometers per hour? Answer: 10 Solution: Emma runs 8 km in 48 minutes. To find speed in km per hour, we need to find how many km she runs in 60 minutes. First, find her speed in km per minute: 8 km ÷ 48 minutes = 1/6 km per minute.
   Full step-by-step solution

   Step 1: Emma runs 8 km in 48 minutes. Step 2: To find speed in km per hour, we need to find how many km she runs in 60 minutes. Step 3: First, find her speed in km per minute: 8 km ÷ 48 minutes = 1/6 km per minute. Step 4: Multiply by 60 minutes to get km per hour: (1/6) × 60 = 10 km per hour. The answer is 10.

2. If 7.5 kilograms of rice cost $33.75, what is the unit rate in dollars per kilogram? Answer: 4.5 Solution: Identify the total cost and total quantity. Total cost = $33.75 Total quantity = 7.5 kg Calculate the unit rate by dividing the total cost by the total quantity.
   Full step-by-step solution

   Step 1: Identify the total cost and total quantity. Total cost = $33.75 Total quantity = 7.5 kg Step 2: Calculate the unit rate by dividing the total cost by the total quantity. Unit rate = Total cost ÷ Total quantity Unit rate = 33.75 ÷ 7.5 Step 3: Perform the division. 33.75 ÷ 7.5 = 4.5 Step 4: State the final answer with the correct units. The unit rate is $4.5 per kilogram.

3. If a car travels 420 miles on 14 gallons of gas, what is the unit rate in miles per gallon? Answer: 30 Solution: Identify the total distance traveled: 420 miles Identify the total gallons used: 14 gallons Calculate the unit rate by dividing total miles by total gallons: 420 ÷ 14 Perform the division: 420 ÷ 14 = 30 The unit rate is 30 miles per gallon.
   Full step-by-step solution

   Step 1: Identify the total distance traveled: 420 miles Step 2: Identify the total gallons used: 14 gallons Step 3: Calculate the unit rate by dividing total miles by total gallons: 420 ÷ 14 Step 4: Perform the division: 420 ÷ 14 = 30 Step 5: The unit rate is 30 miles per gallon.

4. If 7.5 kilograms of rice cost $33.75, what is the unit rate per kilogram? Answer: 4.5 Solution: Identify the total cost and total quantity. Total cost = $33.75, Total quantity = 7.5 kg Calculate the unit rate by dividing total cost by total quantity: 33.75 ÷ 7.5 Perform the division: 33.75 ÷ 7.5 = 4.5 The unit rate is $4.50 per kilogram.
   Full step-by-step solution

   Step 1: Identify the total cost and total quantity. Total cost = $33.75, Total quantity = 7.5 kg Step 2: Calculate the unit rate by dividing total cost by total quantity: 33.75 ÷ 7.5 Step 3: Perform the division: 33.75 ÷ 7.5 = 4.5 Step 4: The unit rate is $4.50 per kilogram. The answer is 4.5.

5. Liam is mixing paint for an art project. He needs to create a specific shade of purple by mixing red and blue paint in a ratio of 3:5. If Liam uses 2.4 liters of blue paint, how many liters of red paint should he use to maintain the correct ratio? Answer: 1.44 Solution: We are told that the ratio of red to blue paint is 3:5. That means for every 3 parts red, there are 5 parts blue. Liam uses 2.4 liters of blue paint.
   Full step-by-step solution

   We are told that the ratio of red to blue paint is 3:5. That means for every 3 parts red, there are 5 parts blue. Liam uses 2.4 liters of blue paint. We need to find how many liters of red paint (let's call it R) will keep the ratio 3:5. Step 1: Set up the proportion Red / Blue = 3 / 5 So R / 2.4 = 3 / 5 Step 2: Solve for R Multiply both sides by 2.4: R = (3 / 5) × 2.4 Step 3: Calculate First, 3 / 5 = 0.6 Then 0.6 × 2.4 = 1.44 Step 4: Conclusion Liam should use 1.44 liters of red paint. ANSWER: 1.44

6. Liam is baking cookies for a school fundraiser. His recipe uses 3 cups of flour to make 24 cookies. If he wants to bake 120 cookies for the event, how many cups of flour will he need? Answer: 15 Solution: First, identify how many cookies are made per cup of flour. The recipe uses 3 cups of flour for 24 cookies. So, cookies per cup = 24 cookies ÷ 3 cups = 8 cookies per cup.
   Full step-by-step solution

   First, identify how many cookies are made per cup of flour. The recipe uses 3 cups of flour for 24 cookies. So, cookies per cup = 24 cookies ÷ 3 cups = 8 cookies per cup. Now, Liam wants 120 cookies. We can set up a proportion: 3 cups / 24 cookies = x cups / 120 cookies. Cross-multiply: 3 * 120 = 24 * x 360 = 24x Divide both sides by 24: x = 360 ÷ 24 x = 15 So, Liam needs 15 cups of flour for 120 cookies.

7. Liam is mixing paint for an art project. He needs to create a specific shade of purple by combining blue and red paint in a ratio of 5:3. If Liam uses 2.5 liters of blue paint, how many liters of red paint should he add to maintain the correct ratio? Answer: 1.5 Solution: The ratio of blue paint to red paint is 5:3. This means for every 5 parts of blue paint, we need 3 parts of red paint. Identify the given quantity.
   Full step-by-step solution

   Let's solve this step by step. Step 1: Understand the ratio. The ratio of blue paint to red paint is 5:3. This means for every 5 parts of blue paint, we need 3 parts of red paint. Step 2: Identify the given quantity. Liam uses 2.5 liters of blue paint. We need to find how many liters of red paint this corresponds to in the ratio. Step 3: Set up the proportion. Let the amount of red paint be R liters. From the ratio: Blue / Red = 5 / 3 So: 2.5 / R = 5 / 3 Step 4: Solve for R. Cross-multiply: 2.5 × 3 = 5 × R 7.5 = 5 × R Divide both sides by 5: R = 7.5 / 5 R = 1.5 Step 5: Conclusion. Liam should add 1.5 liters of red paint to maintain the 5:3 ratio with 2.5 liters of blue paint. Final answer: 1.5

8. Liam is planning a road trip from Boston to Washington D.C. His car's fuel efficiency is 28 miles per gallon on the highway. The total distance is 420 miles. If gasoline costs $3.50 per gallon, how much will Liam spend on gasoline for the one-way trip? Answer: 52.50 Solution: Calculate the total gallons of gasoline needed for the trip. Total distance = 420 miles Fuel efficiency = 28 miles/gallon Gallons needed = Total distance / Fuel efficiency = 420 / 28 420 ÷ 28 = 15 So, Liam needs 15 gallons of gasoline.
   Full step-by-step solution

   Step 1: Calculate the total gallons of gasoline needed for the trip. Total distance = 420 miles Fuel efficiency = 28 miles/gallon Gallons needed = Total distance / Fuel efficiency = 420 / 28 420 ÷ 28 = 15 So, Liam needs 15 gallons of gasoline. Step 2: Calculate the total cost of the gasoline. Cost per gallon = $3.50 Total cost = Gallons needed × Cost per gallon = 15 × 3.50 15 × 3.50 = 52.50 The total cost for gasoline is $52.50.

9. Emma is training for a marathon and tracks her running pace. She runs 4.5 kilometers in 18 minutes. What is her running speed in kilometers per minute? Answer: 0.25 Solution: Identify the given quantities. Distance = 4.5 km, Time = 18 minutes. To find speed in kilometers per minute, divide the total distance by the total time.
   Full step-by-step solution

   Step 1: Identify the given quantities. Distance = 4.5 km, Time = 18 minutes. Step 2: To find speed in kilometers per minute, divide the total distance by the total time. Step 3: Calculation: 4.5 km ÷ 18 minutes = 0.25 km/minute. The answer is 0.25 kilometers per minute.