Unit Rate Applications

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Unit Rate Applications · Grade 6 · Worksheet 2

1. Liam buys 7 kilograms of apples for $15.75. What is the unit price per kilogram? Answer: 2.25 Solution: Total cost = $15.75, total weight = 7 kilograms. Unit price = total cost ÷ total weight = 15.75 ÷ 7. 15.75 ÷ 7 = 2.25.
   Full step-by-step solution

   Step 1: Total cost = $15.75, total weight = 7 kilograms. Step 2: Unit price = total cost ÷ total weight = 15.75 ÷ 7. Step 3: 15.75 ÷ 7 = 2.25. The unit price is $2.25 per kilogram.

2. Ben is training for a bike race. On Saturday, Ben rode her bicycle 50 miles in 5 hours. What was her average speed in miles per hour? Answer: 10 Solution: The total distance is 50 miles and the total time is 5 hours. To find the average speed in miles per hour, divide the distance by the time: 50 miles ÷ 5 hours = 10 miles per hour.
   Full step-by-step solution

   Step 1: The total distance is 50 miles and the total time is 5 hours. Step 2: To find the average speed in miles per hour, divide the distance by the time: 50 miles ÷ 5 hours = 10 miles per hour. The answer is 10 miles per hour.

3. Liam is planning a road trip and needs to calculate his fuel costs. His car can travel 315 miles on 15 gallons of gas. If gas costs $3.60 per gallon, how much will Liam spend on gas to drive 420 miles? Answer: 72 Solution: First, find how many miles Liam's car can travel per gallon of gas. Miles per gallon = Total miles / Total gallons Miles per gallon = 315 / 15 Miles per gallon = 21 So, the car travels 21 miles on 1 gallon of gas.
   Full step-by-step solution

   First, find how many miles Liam's car can travel per gallon of gas. Miles per gallon = Total miles / Total gallons Miles per gallon = 315 / 15 Miles per gallon = 21 So, the car travels 21 miles on 1 gallon of gas. Now, find how many gallons are needed to drive 420 miles. Gallons needed = Total miles / Miles per gallon Gallons needed = 420 / 21 Gallons needed = 20 Gas costs $3.60 per gallon. Total cost = Gallons needed × Cost per gallon Total cost = 20 × 3.60 Total cost = 72 Therefore, Liam will spend $72 on gas.

4. A car travels 360 kilometers in 4 hours. What is its speed in kilometers per hour? Answer: 90 Solution: To find the speed in kilometers per hour, we use the formula: speed = distance / time Identify the distance and time from the problem. The distance traveled is 360 kilometers. The time taken is 4 hours.
   Full step-by-step solution

   To find the speed in kilometers per hour, we use the formula: speed = distance / time Step 1: Identify the distance and time from the problem. The distance traveled is 360 kilometers. The time taken is 4 hours. Step 2: Substitute the values into the formula. speed = 360 km / 4 hours Step 3: Perform the division. 360 divided by 4 equals 90. Step 4: Write the final answer with units. The speed is 90 kilometers per hour.

5. (-24) × 3 ÷ (-8) = ? Answer: 9 Solution: Start with (-24) × 3 A negative times a positive gives a negative: -24 × 3 = -72 Now we have -72 ÷ (-8) A negative divided by a negative gives a positive: -72 ÷ (-8) = 9 The final answer is 9
   Full step-by-step solution

   Step 1: Start with (-24) × 3 Step 2: A negative times a positive gives a negative: -24 × 3 = -72 Step 3: Now we have -72 ÷ (-8) Step 4: A negative divided by a negative gives a positive: -72 ÷ (-8) = 9 Step 5: The final answer is 9

6. Mason drives 1,344 miles in 21 hours. What is the unit rate in miles per hour? Answer: 64 Solution: Identify the total distance: 1,344 miles Identify the total time: 21 hours Divide distance by time: 1,344 ÷ 21 21 × 64 = 1,344, so 1,344 ÷ 21 = 64 The answer is 64 miles per hour.
   Full step-by-step solution

   Step 1: Identify the total distance: 1,344 miles Step 2: Identify the total time: 21 hours Step 3: Divide distance by time: 1,344 ÷ 21 Step 4: 21 × 64 = 1,344, so 1,344 ÷ 21 = 64 The answer is 64 miles per hour.

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 construction company needs to pave a 2.4 kilometer road. Their paving machine can cover 150 meters of road per hour. If the crew works for 8 hours each day, how many days will it take to complete the paving project? Answer: 2 Solution: We need to pave a 2.4 km road. The machine paves 150 meters per hour. The crew works 8 hours per day.
   Full step-by-step solution

   Step 1: Understand the problem We need to pave a 2.4 km road. The machine paves 150 meters per hour. The crew works 8 hours per day. We want the total number of days to finish. Step 2: Convert units to be consistent The road length is given in kilometers, but the paving speed is in meters per hour. So convert 2.4 km to meters: 1 km = 1000 meters 2.4 km = 2.4 × 1000 = 2400 meters. Step 3: Find total hours needed Machine speed = 150 meters per hour. Total hours = Total distance ÷ Speed Total hours = 2400 ÷ 150 2400 ÷ 150 = 16 hours. Step 4: Find total days needed The crew works 8 hours per day. Total days = Total hours ÷ Hours per day Total days = 16 ÷ 8 = 2 days. Step 5: Conclusion It will take 2 days to complete the paving project.

9. A recipe requires 3/4 cup of flour to make 6 cookies. How many cups of flour are needed for 1 cookie? Answer: 0.125 Solution: We know that 3/4 cup of flour makes 6 cookies. To find the flour needed for 1 cookie, we divide the total flour by the number of cookies.
   Full step-by-step solution

   We know that 3/4 cup of flour makes 6 cookies. To find the flour needed for 1 cookie, we divide the total flour by the number of cookies. Step 1: Write the total flour as a fraction: 3/4 cup Step 2: Divide 3/4 by 6: (3/4) ÷ 6 = (3/4) × (1/6) Step 3: Multiply the fractions: (3 × 1) / (4 × 6) = 3 / 24 Step 4: Simplify 3/24: Divide numerator and denominator by 3: 3 ÷ 3 = 1 24 ÷ 3 = 8 So 3/24 = 1/8 Step 5: Convert 1/8 to decimal: 1 ÷ 8 = 0.125 Therefore, the flour needed for 1 cookie is 0.125 cup.