Unit Rates and Comparisons

Maya, Liam, and Benjamin are on a road trip! They're driving a car that travels 240 miles in 4 hours. Can you help them figure out their car's unit rate?

• 80 miles per hour

• 60 miles per hour

• 120 miles per hour

• 40 miles per hour

Answer explanation

The question asks for the unit rate of a car that travels 240 miles in 4 hours. We find the unit rate by dividing the total distance by the total time. So, 240 miles divided by 4 hours gives 60 miles per hour. Therefore, the correct choice is '60 miles per hour'.

Lily, Anika, and Daniel went to a store to buy apples for their apple pie recipe. They found that the store sells 12 apples for $4. Can you help them find the unit rate?

• $0.75 per apple.

• $0.33 per apple

• $0.25 per apple.

• $0.50 per apple.

Answer explanation

The question asks for the unit rate of apples sold in a store. The store sells 12 apples for $4. To find the unit price, we divide the total cost by the quantity. So, $4 divided by 12 apples equals approximately $0.33. Thus, the correct choice is $0.33 per apple.

Aria, Mason, and Hannah are participating in a friendly race. Mason finishes a 5-kilometer race in 25 minutes. Can you help Hannah find out Mason's unit rate?

• 5 kilometers per 5 minutes.

• 2 kilometers per 10 minutes.

• 5 kilometers per 25 minutes

• 10 kilometers per 25 minutes.

Answer explanation

The question asks for the unit rate of a runner who covers a distance of 5 kilometers in 25 minutes. The correct option is '5 kilometers per 25 minutes', since this exactly matches the rate at which the runner is running.

Priya, Aiden, and Nora are having a friendly competition to see who can guess the unit rate of their new soda machine. The machine can produce 500 bottles in 2 hours. Can you help them figure out the unit rate?

• 100 bottles per hour.

• 400 bottles per hour.

• 600 bottles per hour.

• 250 bottles per hour

Answer explanation

The question asks for the unit rate of bottles produced by the machine. The unit rate is found by dividing the total quantity by the total time. Here, the machine produces 500 bottles in 2 hours. So, the unit rate is 500 bottles ÷ 2 hours = 250 bottles per hour, which is the correct answer.

Emma, Nora, and Daniel are having a friendly race. Emma, being a cyclist, covers 30 miles in 2.5 hours. Can you help Nora and Daniel figure out Emma's unit rate?

• 10 miles per hour

• 12 miles per hour

• 20 miles per hour

• 15 miles per hour

Answer explanation

The unit rate is calculated by dividing the total distance by the total time. In this case, the cyclist covers 30 miles in 2.5 hours. When we divide 30 by 2.5, we get 12. So, the unit rate of the cyclist's speed is 12 miles per hour.

Oliver and Aiden decided to have a friendly race with their toy cars. Oliver's car traveled 300 miles in 5 hours, while Aiden's car traveled 240 miles in 4 hours. Mia, who was watching the race, decided to compare the unit rates of both cars. Can you help Mia?

• Both cars have the same unit rate of 60 miles per hour.

• Oliver's car has a unit rate of 70 miles per hour and Aiden's car has a unit rate of 50 miles per hour.

• Oliver's car has a unit rate of 50 miles per hour and Aiden's car has a unit rate of 60 miles per hour.

• Oliver's car has a unit rate of 60 miles per hour and Aiden's car has a unit rate of 50 miles per hour.

Answer explanation

The unit rate is calculated by dividing the total distance by the total time. For the first car, 300 miles divided by 5 hours equals 60 miles per hour. For the second car, 240 miles divided by 4 hours also equals 60 miles per hour. Therefore, both cars have the same unit rate of 60 miles per hour.

Aria, Zoe, and Noah are having a friendly competition to find the best deal on apples. Aria found a store that sells 8 apples for $2, while Zoe found another store that sells 12 apples for $4. Can you help Noah determine who found the better deal?

• The unit rate in Aria's store is $0.50 and the unit rate in Zoe's store is $0.25.

• The unit rate in Aria's store is $0.20 and the unit rate in Zoe's store is $0.40.

• The unit rate in Aria's store is $0.30 and the unit rate in Zoe's store is $0.50.

• The unit rate in Aria's store is $0.25 and the unit rate in Zoe's store is $0.33.

Answer explanation

The unit rate is calculated by dividing the total cost by the number of units. In the first store, divide $2 by 8 apples to get a unit rate of $0.25 per apple. In the second store, divide $4 by 12 apples to get a unit rate of $0.33 per apple. Hence, the correct answer is 'The unit rate in the first store is $0.25 and the unit rate in the second store is $0.33.'

Imagine this! Our friends Daniel and Aria are having a friendly race. Daniel completes a 10-kilometer race in 50 minutes, while Aria finishes a 5-kilometer race in exactly half that time. Nora, who is watching, wonders who is faster. What do you think?

• They both have the same speed.

• They have different speeds.

• They took different times.

• They ran the same distance.

Answer explanation

The first runner runs 10 kilometers in 50 minutes, and the second runner runs 5 kilometers in 25 minutes. When you break it down, both are running at a rate of 1 kilometer every 5 minutes. Therefore, they have the same speed, making the correct answer '

Same speed

'.

David and Oliver are having a friendly competition. David's machine can produce 1000 bottles in 4 hours, while Oliver's machine can produce 500 bottles in 2 hours. Aiden, being the judge, needs to compare the unit rates of both machines. Can you help Aiden?

• Both David and Oliver's machines have the same unit rate of producing 250 bottles per hour.

• Oliver's machine produces more bottles per hour than David's machine.

• David's machine produces more bottles per hour than Oliver's machine.

• Both David and Oliver's machines have the same unit rate of producing 125 bottles per hour.

Answer explanation

The unit rate is found by dividing the total output (bottles) by the total input (hours). For the first machine, this is 1000 bottles / 4 hours = 250 bottles/hour. For the second machine, it's 500 bottles / 2 hours = 250 bottles/hour. Hence, both machines have the same unit rate of producing 250 bottles per hour.

Imagine this! Benjamin and Mia are having a friendly cycling race. Benjamin covers 20 miles in 1.5 hours, while Mia covers 30 miles in 2.5 hours. Avery, who is watching the race, wonders who is cycling at a faster unit rate. Can you help Avery figure it out?

• Both Benjamin and Mia are cycling at the same speed.

• Benjamin is cycling at a faster unit rate.

• Mia is cycling at a faster unit rate.

• The unit rates cannot be compared.

Answer explanation

The unit rate for the first cyclist is 20 miles/1.5 hours = 13.33 miles per hour, while the second cyclist's unit rate is 30 miles/2.5 hours = 12 miles per hour. Therefore, the first cyclist covers more distance in the same amount of time, making them the correct choice.