Here are the step-by-step solutions for each problem on the worksheet.
1. I write about 12 emails per day. How long will it take me to write 60 emails?
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Step 1: Identify the rate. You write 12 emails in 1 day.
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Step 2: Identify the goal. You need to write 60 emails.
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Step 3: Divide the total number of emails by the number of emails per day to find the number of days.
* $60 \div 12 = 5$
*
Result: It will take 5 days.
2. Peter can run 10 kilometers in 2 hours at a steady rate. How long will it take him to run 30 kilometers?
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Step 1: Find Peter's speed (unit rate). Divide the distance by the time.
* $10 \text{ km} \div 2 \text{ hours} = 5 \text{ km per hour}$.
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Step 2: Use this speed to find the time for the new distance. Divide the new distance (30 km) by the speed (5 km/h).
* $30 \div 5 = 6$
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Result: It will take 6 hours.
3. I can wash a car in 20 minutes. How long will it take me to wash 20 cars?
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Step 1: Identify the time per car. It takes 20 minutes for 1 car.
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Step 2: Multiply the time per car by the total number of cars.
* $20 \text{ minutes} \times 20 \text{ cars} = 400 \text{ minutes}$.
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Step 3 (Optional but good): Convert minutes to hours and minutes.
* $400 \div 60 = 6$ with a remainder of $40$.
* So, 6 hours and 40 minutes.
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Result: It will take 400 minutes (or 6 hours and 40 minutes).
4. I can type 4 words per minute. How long will it take me to write an 500 words essay?
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Step 1: Identify the typing speed. 4 words per minute.
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Step 2: Divide the total number of words by the speed.
* $500 \div 4$
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Step 3: Calculate the division.
* $500 \div 2 = 250$
* $250 \div 2 = 125$
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Result: It will take 125 minutes. (This is also 2 hours and 5 minutes).
5. A baker can bake 20 cakes per hour. How long will it take him to bake 400 cakes?
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Step 1: Identify the baking rate. 20 cakes per 1 hour.
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Step 2: Divide the total number of cakes by the rate.
* $400 \div 20$
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Step 3: Simplify the division. You can cross out the zeros: $40 \div 2 = 20$.
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Result: It will take 20 hours.
6. It takes me 10 minutes to swim 2 laps. How long will it take me to swim 5 laps?
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Step 1: Find the time it takes to swim just 1 lap (the unit rate).
* $10 \text{ minutes} \div 2 \text{ laps} = 5 \text{ minutes per lap}$.
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Step 2: Multiply the time per lap by the new number of laps (5).
* $5 \text{ minutes} \times 5 \text{ laps} = 25 \text{ minutes}$.
*
Result: It will take 25 minutes.
Final Answer:
1. 5 days
2. 6 hours
3. 400 minutes (or 6 hours and 40 minutes)
4. 125 minutes (or 2 hours and 5 minutes)
5. 20 hours
6. 25 minutes
Parent Tip: Review the logic above to help your child master the concept of ratio and rate problems worksheet.
