Printable worksheet titled "Unit Rate Word Problems" featuring six real-world math problems requiring students to calculate rates and solve for time, distance, and cost.
Unit Rate Word Problems worksheet with six math problems involving rates, including reading speed, car speed, production rates, baking time, price calculation, and walking speed.
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Step-by-step solution for: Printable primary math worksheet for math grades 1 to 6 based on ...
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Show Answer Key & Explanations
Step-by-step solution for: Printable primary math worksheet for math grades 1 to 6 based on ...
Let's solve each problem step by step:
---
I can read 120 words per 12 minutes. How many hours will it take me to read a book with 6,000 words?
#### Solution:
1. Find the reading rate in words per minute:
\[
\text{Words per minute} = \frac{120 \text{ words}}{12 \text{ minutes}} = 10 \text{ words per minute}
\]
2. Calculate the total time needed to read 6,000 words:
\[
\text{Total time (in minutes)} = \frac{6,000 \text{ words}}{10 \text{ words per minute}} = 600 \text{ minutes}
\]
3. Convert minutes to hours:
\[
\text{Total time (in hours)} = \frac{600 \text{ minutes}}{60 \text{ minutes per hour}} = 10 \text{ hours}
\]
Answer:
\[
\boxed{10}
\]
---
A car’s top speed is 120 miles per hour. How many minutes will it take the car to drive 50 miles at top speed?
#### Solution:
1. Find the time taken to travel 50 miles:
\[
\text{Time (in hours)} = \frac{\text{Distance}}{\text{Speed}} = \frac{50 \text{ miles}}{120 \text{ miles per hour}} = \frac{5}{12} \text{ hours}
\]
2. Convert hours to minutes:
\[
\text{Time (in minutes)} = \frac{5}{12} \times 60 = 25 \text{ minutes}
\]
Answer:
\[
\boxed{25}
\]
---
A car factory can produce 3 cars per 2 minutes. If the factory opens for production at 8:30 am and closes at 5:30 pm, how many cars can the factory produce in a day?
#### Solution:
1. Calculate the total production time in minutes:
- The factory operates from 8:30 am to 5:30 pm.
- Total time = \(5:30 \text{ pm} - 8:30 \text{ am} = 9 \text{ hours}\).
- Convert hours to minutes:
\[
9 \text{ hours} \times 60 \text{ minutes per hour} = 540 \text{ minutes}
\]
2. Find the production rate in cars per minute:
\[
\text{Cars per minute} = \frac{3 \text{ cars}}{2 \text{ minutes}} = 1.5 \text{ cars per minute}
\]
3. Calculate the total number of cars produced in 540 minutes:
\[
\text{Total cars} = 1.5 \text{ cars per minute} \times 540 \text{ minutes} = 810 \text{ cars}
\]
Answer:
\[
\boxed{810}
\]
---
A bakery store can bake 12 breads per hour. How many minutes does it take the bakery to bake 3 breads?
#### Solution:
1. Find the baking rate in breads per minute:
\[
\text{Breads per minute} = \frac{12 \text{ breads}}{60 \text{ minutes}} = 0.2 \text{ breads per minute}
\]
2. Calculate the time needed to bake 3 breads:
\[
\text{Time (in minutes)} = \frac{3 \text{ breads}}{0.2 \text{ breads per minute}} = 15 \text{ minutes}
\]
Answer:
\[
\boxed{15}
\]
---
In the supermarket, the price of 4 kilograms of sugar is $3. What is the price of 120 kilograms of sugar?
#### Solution:
1. Find the price per kilogram of sugar:
\[
\text{Price per kilogram} = \frac{\$3}{4 \text{ kilograms}} = \$0.75 \text{ per kilogram}
\]
2. Calculate the price of 120 kilograms:
\[
\text{Total price} = 120 \text{ kilograms} \times \$0.75 \text{ per kilogram} = \$90
\]
Answer:
\[
\boxed{90}
\]
---
I can walk 20 kilometers in 5 hours. If I walk at this speed, how long will it take me to walk 200 meters?
#### Solution:
1. Find the walking speed in kilometers per hour:
\[
\text{Speed} = \frac{20 \text{ kilometers}}{5 \text{ hours}} = 4 \text{ kilometers per hour}
\]
2. Convert 200 meters to kilometers:
\[
200 \text{ meters} = \frac{200}{1000} \text{ kilometers} = 0.2 \text{ kilometers}
\]
3. Calculate the time needed to walk 0.2 kilometers:
\[
\text{Time (in hours)} = \frac{\text{Distance}}{\text{Speed}} = \frac{0.2 \text{ kilometers}}{4 \text{ kilometers per hour}} = 0.05 \text{ hours}
\]
4. Convert hours to minutes:
\[
\text{Time (in minutes)} = 0.05 \text{ hours} \times 60 \text{ minutes per hour} = 3 \text{ minutes}
\]
Answer:
\[
\boxed{3}
\]
---
1. \(\boxed{10}\)
2. \(\boxed{25}\)
3. \(\boxed{810}\)
4. \(\boxed{15}\)
5. \(\boxed{90}\)
6. \(\boxed{3}\)
---
Problem 1:
I can read 120 words per 12 minutes. How many hours will it take me to read a book with 6,000 words?
#### Solution:
1. Find the reading rate in words per minute:
\[
\text{Words per minute} = \frac{120 \text{ words}}{12 \text{ minutes}} = 10 \text{ words per minute}
\]
2. Calculate the total time needed to read 6,000 words:
\[
\text{Total time (in minutes)} = \frac{6,000 \text{ words}}{10 \text{ words per minute}} = 600 \text{ minutes}
\]
3. Convert minutes to hours:
\[
\text{Total time (in hours)} = \frac{600 \text{ minutes}}{60 \text{ minutes per hour}} = 10 \text{ hours}
\]
Answer:
\[
\boxed{10}
\]
---
Problem 2:
A car’s top speed is 120 miles per hour. How many minutes will it take the car to drive 50 miles at top speed?
#### Solution:
1. Find the time taken to travel 50 miles:
\[
\text{Time (in hours)} = \frac{\text{Distance}}{\text{Speed}} = \frac{50 \text{ miles}}{120 \text{ miles per hour}} = \frac{5}{12} \text{ hours}
\]
2. Convert hours to minutes:
\[
\text{Time (in minutes)} = \frac{5}{12} \times 60 = 25 \text{ minutes}
\]
Answer:
\[
\boxed{25}
\]
---
Problem 3:
A car factory can produce 3 cars per 2 minutes. If the factory opens for production at 8:30 am and closes at 5:30 pm, how many cars can the factory produce in a day?
#### Solution:
1. Calculate the total production time in minutes:
- The factory operates from 8:30 am to 5:30 pm.
- Total time = \(5:30 \text{ pm} - 8:30 \text{ am} = 9 \text{ hours}\).
- Convert hours to minutes:
\[
9 \text{ hours} \times 60 \text{ minutes per hour} = 540 \text{ minutes}
\]
2. Find the production rate in cars per minute:
\[
\text{Cars per minute} = \frac{3 \text{ cars}}{2 \text{ minutes}} = 1.5 \text{ cars per minute}
\]
3. Calculate the total number of cars produced in 540 minutes:
\[
\text{Total cars} = 1.5 \text{ cars per minute} \times 540 \text{ minutes} = 810 \text{ cars}
\]
Answer:
\[
\boxed{810}
\]
---
Problem 4:
A bakery store can bake 12 breads per hour. How many minutes does it take the bakery to bake 3 breads?
#### Solution:
1. Find the baking rate in breads per minute:
\[
\text{Breads per minute} = \frac{12 \text{ breads}}{60 \text{ minutes}} = 0.2 \text{ breads per minute}
\]
2. Calculate the time needed to bake 3 breads:
\[
\text{Time (in minutes)} = \frac{3 \text{ breads}}{0.2 \text{ breads per minute}} = 15 \text{ minutes}
\]
Answer:
\[
\boxed{15}
\]
---
Problem 5:
In the supermarket, the price of 4 kilograms of sugar is $3. What is the price of 120 kilograms of sugar?
#### Solution:
1. Find the price per kilogram of sugar:
\[
\text{Price per kilogram} = \frac{\$3}{4 \text{ kilograms}} = \$0.75 \text{ per kilogram}
\]
2. Calculate the price of 120 kilograms:
\[
\text{Total price} = 120 \text{ kilograms} \times \$0.75 \text{ per kilogram} = \$90
\]
Answer:
\[
\boxed{90}
\]
---
Problem 6:
I can walk 20 kilometers in 5 hours. If I walk at this speed, how long will it take me to walk 200 meters?
#### Solution:
1. Find the walking speed in kilometers per hour:
\[
\text{Speed} = \frac{20 \text{ kilometers}}{5 \text{ hours}} = 4 \text{ kilometers per hour}
\]
2. Convert 200 meters to kilometers:
\[
200 \text{ meters} = \frac{200}{1000} \text{ kilometers} = 0.2 \text{ kilometers}
\]
3. Calculate the time needed to walk 0.2 kilometers:
\[
\text{Time (in hours)} = \frac{\text{Distance}}{\text{Speed}} = \frac{0.2 \text{ kilometers}}{4 \text{ kilometers per hour}} = 0.05 \text{ hours}
\]
4. Convert hours to minutes:
\[
\text{Time (in minutes)} = 0.05 \text{ hours} \times 60 \text{ minutes per hour} = 3 \text{ minutes}
\]
Answer:
\[
\boxed{3}
\]
---
Final Answers:
1. \(\boxed{10}\)
2. \(\boxed{25}\)
3. \(\boxed{810}\)
4. \(\boxed{15}\)
5. \(\boxed{90}\)
6. \(\boxed{3}\)
Parent Tip: Review the logic above to help your child master the concept of unit rate word problems worksheet.