Question
Polly and Amira are trying for a bike race. Polly bikes, 30 miles and four hours. Amira like 24 miles and three hours. Assuming that they each travel at constant speed, who biked at a faster rate?
Answers
GPT-4o
To determine who biked at a faster rate, we'll calculate the speed for both Polly and Amira.
**Polly:**
- Distance: 30 miles
- Time: 4 hours
Speed = \(\frac{\text{Distance}}{\text{Time}}\)
Polly's speed:
\[ \text{Speed} = \frac{30 \text{ miles}}{4 \text{ hours}} = 7.5 \text{ miles per hour} \]
**Amira:**
- Distance: 24 miles
- Time: 3 hours
Speed = \(\frac{\text{Distance}}{\text{Time}}\)
Amira's speed:
\[ \text{Speed} = \frac{24 \text{ miles}}{3 \text{ hours}} = 8 \text{ miles per hour} \]
Comparing the two speeds:
- Polly's speed: 7.5 miles per hour
- Amira's speed: 8 miles per hour
Amira biked at a faster rate than Polly.
**Polly:**
- Distance: 30 miles
- Time: 4 hours
Speed = \(\frac{\text{Distance}}{\text{Time}}\)
Polly's speed:
\[ \text{Speed} = \frac{30 \text{ miles}}{4 \text{ hours}} = 7.5 \text{ miles per hour} \]
**Amira:**
- Distance: 24 miles
- Time: 3 hours
Speed = \(\frac{\text{Distance}}{\text{Time}}\)
Amira's speed:
\[ \text{Speed} = \frac{24 \text{ miles}}{3 \text{ hours}} = 8 \text{ miles per hour} \]
Comparing the two speeds:
- Polly's speed: 7.5 miles per hour
- Amira's speed: 8 miles per hour
Amira biked at a faster rate than Polly.
Ariana and Jared are each entering their homemade tomato sauce and a cooking contest. Ariana‘s recipe uses 15 tablespoons of fresh basil for 6 quarts of sauce. Jared recipe uses 9 tablespoons of fresh basil for 4 quarts of sauce. Who uses more basil per quart of sauce?
GPT-4o
To determine who uses more basil per quart of sauce, we'll calculate the amount of basil used per quart for both Ariana and Jared.
**Ariana:**
- Basil: 15 tablespoons
- Sauce: 6 quarts
Basil per quart for Ariana:
\[ \text{Basil per quart} = \frac{15 \text{ tablespoons}}{6 \text{ quarts}} = 2.5 \text{ tablespoons per quart} \]
**Jared:**
- Basil: 9 tablespoons
- Sauce: 4 quarts
Basil per quart for Jared:
\[ \text{Basil per quart} = \frac{9 \text{ tablespoons}}{4 \text{ quarts}} = 2.25 \text{ tablespoons per quart} \]
Comparing the two:
- Ariana: 2.5 tablespoons per quart
- Jared: 2.25 tablespoons per quart
Ariana uses more basil per quart of sauce than Jared.
**Ariana:**
- Basil: 15 tablespoons
- Sauce: 6 quarts
Basil per quart for Ariana:
\[ \text{Basil per quart} = \frac{15 \text{ tablespoons}}{6 \text{ quarts}} = 2.5 \text{ tablespoons per quart} \]
**Jared:**
- Basil: 9 tablespoons
- Sauce: 4 quarts
Basil per quart for Jared:
\[ \text{Basil per quart} = \frac{9 \text{ tablespoons}}{4 \text{ quarts}} = 2.25 \text{ tablespoons per quart} \]
Comparing the two:
- Ariana: 2.5 tablespoons per quart
- Jared: 2.25 tablespoons per quart
Ariana uses more basil per quart of sauce than Jared.
Employee is at scrumptious smoothies use 4 cups of strawberries to make eight strawberry bananas smoothies. Make four kiwi, strawberry smoothies, they use 3 cups of strawberries. Which flavor uses more cups of strawberries per smoothie, strawberry banana or kiwi strawberry?
GPT-4o
To determine which flavor uses more cups of strawberries per smoothie, we'll calculate the amount of strawberries used per smoothie for both the Strawberry Banana and the Kiwi Strawberry flavors.
**Strawberry Banana:**
- Cups of strawberries: 4 cups
- Number of smoothies: 8 smoothies
Strawberries per smoothie for Strawberry Banana:
\[ \text{Strawberries per smoothie} = \frac{4 \text{ cups}}{8 \text{ smoothies}} = 0.5 \text{ cups per smoothie} \]
**Kiwi Strawberry:**
- Cups of strawberries: 3 cups
- Number of smoothies: 4 smoothies
Strawberries per smoothie for Kiwi Strawberry:
\[ \text{Strawberries per smoothie} = \frac{3 \text{ cups}}{4 \text{ smoothies}} = 0.75 \text{ cups per smoothie} \]
Comparing the amounts:
- Strawberry Banana: 0.5 cups per smoothie
- Kiwi Strawberry: 0.75 cups per smoothie
The Kiwi Strawberry flavor uses more cups of strawberries per smoothie than the Strawberry Banana flavor.
**Strawberry Banana:**
- Cups of strawberries: 4 cups
- Number of smoothies: 8 smoothies
Strawberries per smoothie for Strawberry Banana:
\[ \text{Strawberries per smoothie} = \frac{4 \text{ cups}}{8 \text{ smoothies}} = 0.5 \text{ cups per smoothie} \]
**Kiwi Strawberry:**
- Cups of strawberries: 3 cups
- Number of smoothies: 4 smoothies
Strawberries per smoothie for Kiwi Strawberry:
\[ \text{Strawberries per smoothie} = \frac{3 \text{ cups}}{4 \text{ smoothies}} = 0.75 \text{ cups per smoothie} \]
Comparing the amounts:
- Strawberry Banana: 0.5 cups per smoothie
- Kiwi Strawberry: 0.75 cups per smoothie
The Kiwi Strawberry flavor uses more cups of strawberries per smoothie than the Strawberry Banana flavor.
Make bot 4 1/2 yards of fabric to make purses to sell a craft fair. Each purse will use 1/3 of the fabric meg bot. How much fabric will be used for each purse?
GPT-4o
To determine how much fabric will be used for each purse, we'll calculate \(\frac{1}{3}\) of the total fabric Meg bought.
Meg bought \(4 \frac{1}{2}\) yards, which is equivalent to \(4.5\) yards.
To find \(\frac{1}{3}\) of this fabric:
\[ \frac{1}{3} \times 4.5 \text{ yards} = \frac{4.5}{3} \text{ yards} = 1.5 \text{ yards} \]
So, each purse will use 1.5 yards of fabric.
Meg bought \(4 \frac{1}{2}\) yards, which is equivalent to \(4.5\) yards.
To find \(\frac{1}{3}\) of this fabric:
\[ \frac{1}{3} \times 4.5 \text{ yards} = \frac{4.5}{3} \text{ yards} = 1.5 \text{ yards} \]
So, each purse will use 1.5 yards of fabric.
Noah and Jasmine are learning how to net scarves. Noah scarf is one and a half feet long. Jasmine scarf is 2 1/2 times that length. How long is Jasmine scarf?
GPT-4o
To find out how long Jasmine's scarf is, we need to calculate \(2 \frac{1}{2}\) times the length of Noah's scarf.
Noah's scarf length:
\[ 1 \frac{1}{2} \text{ feet} = 1.5 \text{ feet} \]
Jasmine's scarf is \(2 \frac{1}{2}\) times Noah's scarf length, which is:
\[ 2 \frac{1}{2} = 2 + \frac{1}{2} = 2.5 \]
Now, multiply the length of Noah's scarf by \(2.5\):
\[ 2.5 \times 1.5 = 3.75 \text{ feet} \]
Jasmine's scarf is 3.75 feet long.
Noah's scarf length:
\[ 1 \frac{1}{2} \text{ feet} = 1.5 \text{ feet} \]
Jasmine's scarf is \(2 \frac{1}{2}\) times Noah's scarf length, which is:
\[ 2 \frac{1}{2} = 2 + \frac{1}{2} = 2.5 \]
Now, multiply the length of Noah's scarf by \(2.5\):
\[ 2.5 \times 1.5 = 3.75 \text{ feet} \]
Jasmine's scarf is 3.75 feet long.
Brian soccer team has played 12 games this year. They won 3/4 of their games. At the games they won, they celebration with pizza after 2/3 of them. How many games did Brian‘s team celebrate with pizza?
GPT-4o
To find out how many games Brian's team celebrated with pizza, we'll follow these steps:
1. Determine the number of games they won.
2. Determine the number of games they celebrated with pizza.
**Step 1: Determine the number of games they won.**
The team won \(\frac{3}{4}\) of their games.
Number of games won:
\[ \frac{3}{4} \times 12 = 9 \text{ games} \]
**Step 2: Determine the number of games they celebrated with pizza.**
They celebrated with pizza after \(\frac{2}{3}\) of the games they won.
Number of games celebrated with pizza:
\[ \frac{2}{3} \times 9 = 6 \text{ games} \]
Brian's team celebrated with pizza after 6 games.
1. Determine the number of games they won.
2. Determine the number of games they celebrated with pizza.
**Step 1: Determine the number of games they won.**
The team won \(\frac{3}{4}\) of their games.
Number of games won:
\[ \frac{3}{4} \times 12 = 9 \text{ games} \]
**Step 2: Determine the number of games they celebrated with pizza.**
They celebrated with pizza after \(\frac{2}{3}\) of the games they won.
Number of games celebrated with pizza:
\[ \frac{2}{3} \times 9 = 6 \text{ games} \]
Brian's team celebrated with pizza after 6 games.