Unit Rate Applications

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Unit Rate Applications · Grade 6 · Worksheet 2

1. Liam is planning a road trip and needs to calculate his fuel costs. His car can travel 315 miles on 15 gallons of gasoline. If the current price of gasoline is $3.50 per gallon, how much would it cost Liam to drive 840 miles? Answer: $140 Solution: First, find how many miles Liam's car travels per gallon of gasoline. Miles per gallon = Total miles / Total gallons Miles per gallon = 315 / 15 Miles per gallon = 21 This means the car travels 21 miles on 1 gallon of gasoline.
   Full step-by-step solution

   First, find how many miles Liam's car travels per gallon of gasoline. Miles per gallon = Total miles / Total gallons Miles per gallon = 315 / 15 Miles per gallon = 21 This means the car travels 21 miles on 1 gallon of gasoline. Next, find how many gallons are needed to drive 840 miles. Gallons needed = Total miles / Miles per gallon Gallons needed = 840 / 21 Gallons needed = 40 Now, calculate the cost for 40 gallons of gasoline. Cost = Gallons needed × Price per gallon Cost = 40 × 3.50 Cost = 140 So, the total cost for Liam to drive 840 miles is $140.

2. Aisha is organizing a community garden project and needs to calculate fertilizer costs. The garden area is 1,800 square meters, and the fertilizer instructions recommend using 0.25 kilograms per 30 square meters. If fertilizer costs $4.80 per kilogram, and Aisha wants to buy an extra 10% to account for spillage and uneven application, how much will she spend on fertilizer in total? Answer: $79.20 Solution: Calculate the fertilizer needed for the garden area. Fertilizer per square meter = 0.25 kg / 30 sq m = 0.008333 kg/sq m Total fertilizer for 1,800 sq m = 0.008333 kg/sq m × 1,800 sq m = 15 kg Add 10% extra for spillage and uneven application.
   Full step-by-step solution

   Step 1: Calculate the fertilizer needed for the garden area. Fertilizer per square meter = 0.25 kg / 30 sq m = 0.008333 kg/sq m Total fertilizer for 1,800 sq m = 0.008333 kg/sq m × 1,800 sq m = 15 kg Step 2: Add 10% extra for spillage and uneven application. Extra fertilizer = 15 kg × 0.10 = 1.5 kg Total fertilizer to buy = 15 kg + 1.5 kg = 16.5 kg Step 3: Calculate the total cost. Cost = 16.5 kg × $4.80/kg = $79.20 The answer is $79.20.

3. Sophia earns $1,344 for working 56 hours. What is her unit rate of pay per hour? Answer: 24 Solution: Total earnings = $1,344 Total hours worked = 56 hours Unit rate = 1,344 ÷ 56 1,344 ÷ 56 = 24 The answer is $24 per hour.
   Full step-by-step solution

   Step 1: Total earnings = $1,344 Step 2: Total hours worked = 56 hours Step 3: Unit rate = 1,344 ÷ 56 Step 4: 1,344 ÷ 56 = 24 The answer is $24 per hour.

4. Liam is making a large batch of lemonade for a school event. His recipe requires 3.5 cups of lemon juice to make 14 servings. If he needs to prepare enough lemonade for 60 students, how many cups of lemon juice should he use? Answer: 15 Solution: First, find how many cups of lemon juice are needed per serving. The recipe uses 3.5 cups for 14 servings. So, cups per serving = 3.5 cups ÷ 14 servings.
   Full step-by-step solution

   First, find how many cups of lemon juice are needed per serving. The recipe uses 3.5 cups for 14 servings. So, cups per serving = 3.5 cups ÷ 14 servings. 3.5 ÷ 14 = 0.25 cups per serving. Now, Liam needs to make lemonade for 60 students, meaning 60 servings. Multiply the cups per serving by the number of servings needed: 0.25 cups/serving × 60 servings = 15 cups. So, Liam should use 15 cups of lemon juice.

5. A triangular prism is drawn with a right triangular base. The triangular base has legs measuring 6 cm and 8 cm, and the prism has a height of 12 cm. What is the volume of this prism in cubic centimeters? Answer: 288 Solution: Find the area of the triangular base. The formula for area of a right triangle is (1/2) × leg1 × leg2. Area of base = (1/2) × 6 cm × 8 cm = (1/2) × 48 cm² = 24 cm².
   Full step-by-step solution

   Step 1: Find the area of the triangular base. The formula for area of a right triangle is (1/2) × leg1 × leg2. Step 2: Area of base = (1/2) × 6 cm × 8 cm = (1/2) × 48 cm² = 24 cm². Step 3: Find the volume of the prism. The formula for volume of any prism is area of base × height. Step 4: Volume = 24 cm² × 12 cm = 288 cm³. The volume of the triangular prism is 288 cubic centimeters.

6. A rectangular prism is drawn with dimensions: length = 12 cm, width = 8 cm, and height = 5 cm. If you were to draw a net of this prism and cut it out, what would be the total surface area of all the faces combined? Answer: 392 Solution: - Two faces with dimensions 12 cm by 8 cm - Two faces with dimensions 12 cm by 5 cm - Two faces with dimensions 8 cm by 5 cm - Area of one 12×8 face = 12 × 8 = 96 cm² - Total for both 12×8 faces = 2 × 96 = 192 cm² - Area of one 12×5 face = 12 × 5 = 60 cm² - Total for both 12×5 faces = 2 × 60 =…
   Full step-by-step solution

   Step 1: Identify the three pairs of identical faces: - Two faces with dimensions 12 cm by 8 cm - Two faces with dimensions 12 cm by 5 cm - Two faces with dimensions 8 cm by 5 cm Step 2: Calculate the area for each pair: - Area of one 12×8 face = 12 × 8 = 96 cm² - Total for both 12×8 faces = 2 × 96 = 192 cm² - Area of one 12×5 face = 12 × 5 = 60 cm² - Total for both 12×5 faces = 2 × 60 = 120 cm² - Area of one 8×5 face = 8 × 5 = 40 cm² - Total for both 8×5 faces = 2 × 40 = 80 cm² Step 3: Sum all the areas: Total surface area = 192 + 120 + 80 = 392 cm² The answer is 392.

7. Liam is planning a road trip and needs to calculate his fuel costs. His car can travel 315 miles on 15 gallons of gasoline. If the current price of gasoline is $3.50 per gallon, how much will it cost him in dollars to drive 420 miles? Answer: 70 Solution: Find the car's fuel efficiency (miles per gallon). The car travels 315 miles on 15 gallons. Miles per gallon = 315 / 15 = 21 miles per gallon.
   Full step-by-step solution

   Step 1: Find the car's fuel efficiency (miles per gallon). The car travels 315 miles on 15 gallons. Miles per gallon = 315 / 15 = 21 miles per gallon. Step 2: Find how many gallons are needed to drive 420 miles. Gallons needed = Total miles / Miles per gallon = 420 / 21 = 20 gallons. Step 3: Calculate the cost. Price per gallon = $3.50. Total cost = Gallons needed × Price per gallon = 20 × 3.50 = 70 dollars. Final answer: 70

8. A factory produces 1,560 units of a product in 6.5 hours. The factory manager wants to calculate the production rate per minute to optimize the assembly line. How many units does the factory produce per minute? Answer: 4 Solution: First, convert the total time from hours to minutes. Since there are 60 minutes in an hour, 6.5 hours is 6.5 × 60 = 390 minutes. The factory produces 1,560 units in 390 minutes.
   Full step-by-step solution

   Step 1: First, convert the total time from hours to minutes. Since there are 60 minutes in an hour, 6.5 hours is 6.5 × 60 = 390 minutes. Step 2: The factory produces 1,560 units in 390 minutes. Step 3: To find the production rate per minute, divide the total number of units by the total number of minutes: 1,560 ÷ 390. Step 4: Calculate 1,560 ÷ 390 = 4. The factory produces 4 units per minute.