Unit Rate Applications

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Unit Rate Applications · Grade 6 · Worksheet 3

1. 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.

2. (-18) × 2 ÷ (-9) = ? Answer: 4 Solution: Multiply -18 by 2: (-18) × 2 = -36 Divide -36 by -9: -36 ÷ (-9) = 4 Since dividing two negative numbers gives a positive result, the answer is 4.
   Full step-by-step solution

   Step 1: Multiply -18 by 2: (-18) × 2 = -36 Step 2: Divide -36 by -9: -36 ÷ (-9) = 4 Step 3: Since dividing two negative numbers gives a positive result, the answer is 4.

3. A triangular garden is drawn on a coordinate plane with vertices at (0,0), (12,0), and (0,5). If each unit on the grid represents 4 feet, what is the actual area of the garden in square feet? Answer: 480 Solution: Identify the triangle's base and height from the coordinates. The base is along the x-axis from (0,0) to (12,0), so the base is 12 units. The height is along the y-axis from (0,0) to (0,5), so the height is 5 units.
   Full step-by-step solution

   Step 1: Identify the triangle's base and height from the coordinates. The base is along the x-axis from (0,0) to (12,0), so the base is 12 units. The height is along the y-axis from (0,0) to (0,5), so the height is 5 units. Step 2: Calculate the area of the triangle on the coordinate grid using the formula: Area = (1/2) × base × height = (1/2) × 12 × 5 = (1/2) × 60 = 30 square units. Step 3: Apply the scale factor. Each unit represents 4 feet, so for area, we need to square the scale factor: 4 feet/unit × 4 feet/unit = 16 square feet/square unit. Step 4: Multiply the grid area by the squared scale factor: 30 square units × 16 square feet/square unit = 480 square feet. The actual area of the garden is 480 square feet.

4. A factory produces 1,680 units of a product in 7 hours. If the factory needs to fill an order for 3,600 units and can only operate for 12 hours today, will they meet the production goal? If not, how many additional units will they need to produce tomorrow? Answer: No, 120 units Solution: Find the unit rate per hour: 1,680 units ÷ 7 hours = 240 units per hour Calculate production in 12 hours: 240 units/hour × 12 hours = 2,880 units Compare to order requirement: 3,600 units needed - 2,880 units produced = 720 units short The factory will not meet the goal and needs to produce 720…
   Full step-by-step solution

   Step 1: Find the unit rate per hour: 1,680 units ÷ 7 hours = 240 units per hour Step 2: Calculate production in 12 hours: 240 units/hour × 12 hours = 2,880 units Step 3: Compare to order requirement: 3,600 units needed - 2,880 units produced = 720 units short Step 4: The factory will not meet the goal and needs to produce 720 additional units tomorrow.

5. Noah earns $2,184 for working 42 hours. What is his unit rate of pay in dollars per hour? Answer: 52 Solution: Identify the total amount earned: $2,184 Identify the total hours worked: 42 hours Divide the total earnings by the total hours to find the unit rate: 2184 ÷ 42 Perform the division: 42 × 50 = 2100, remainder 84; 42 × 2 = 84, remainder 0; so 2184 ÷ 42 = 52 The unit rate is $52 per hour.
   Full step-by-step solution

   Step 1: Identify the total amount earned: $2,184 Step 2: Identify the total hours worked: 42 hours Step 3: Divide the total earnings by the total hours to find the unit rate: 2184 ÷ 42 Step 4: Perform the division: 42 × 50 = 2100, remainder 84; 42 × 2 = 84, remainder 0; so 2184 ÷ 42 = 52 Step 5: The unit rate is $52 per hour. The answer is 52.

6. 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.

7. (-18) × 2 ÷ (-3) = ? Answer: 12 Solution: Multiply -18 by 2: (-18) × 2 = -36 Divide -36 by -3: -36 ÷ (-3) = 12 Since dividing two negative numbers gives a positive result, the answer is 12.
   Full step-by-step solution

   Step 1: Multiply -18 by 2: (-18) × 2 = -36 Step 2: Divide -36 by -3: -36 ÷ (-3) = 12 Step 3: Since dividing two negative numbers gives a positive result, the answer is 12.

8. 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 the current price of gas is $3.60 per gallon, how much will it cost him in dollars to drive 420 miles? Answer: 72 Solution: The car travels 315 miles on 15 gallons. Miles per gallon = 315 / 15 315 ÷ 15 = 21 So the car gets 21 miles per gallon.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Find the car's fuel efficiency (miles per gallon)** The car travels 315 miles on 15 gallons. Miles per gallon = 315 / 15 315 ÷ 15 = 21 So the car gets 21 miles per gallon. --- **Step 2: Find gallons needed for 420 miles** Gallons needed = (miles to travel) / (miles per gallon) Gallons needed = 420 / 21 420 ÷ 21 = 20 So Liam needs 20 gallons for 420 miles. --- **Step 3: Calculate cost** Price per gallon = $3.60 Total cost = (gallons needed) × (price per gallon) Total cost = 20 × 3.60 20 × 3.60 = 72.00 --- **Final answer:** 72

9. (-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