Answered

1. It takes Maya 30 minutes to solve 5 logic puzzles, and it takes Amy 28 minutes to solve 4 logic puzzles. Use models to show the rate at which each student solves the puzzles, in minutes per puzzle.

[tex]\[
\begin{aligned}
30 \div 5 &= 6 \text{ minutes per puzzle (Maya)} \\
28 \div 4 &= 7 \text{ minutes per puzzle (Amy)}
\end{aligned}
\][/tex]

If Maya and Amy had the same number of puzzles to solve, who would finish first? Explain.

2. A garden hose supplies 36 gallons of water in 3 minutes. Use a table of equivalent ratios to show the garden hose's water flow in gallons per minute and minutes per gallon.

[tex]\[
\begin{aligned}
\text{Gallons per minute:} & \\
\frac{36 \text{ gallons}}{3 \text{ minutes}} &= 12 \text{ gallons per minute} \\
\text{Minutes per gallon:} & \\
\frac{3 \text{ minutes}}{36 \text{ gallons}} &= 0.083 \text{ minutes per gallon}
\end{aligned}
\][/tex]



Answer :

GinnyAnswer
Certainly! Let's solve the problem step-by-step and provide detailed explanations for each part.

### Part 1: Rate at Which Each Student Solves the Puzzles

#### 1.1. Calculating Maya's Puzzle Solving Rate
Maya takes 30 minutes to solve 5 puzzles.
We need to find the rate in minutes per puzzle, which is calculated by dividing the total time by the number of puzzles:

[tex]\[ \text{Maya's rate} = \frac{30 \text{ minutes}}{5 \text{ puzzles}} = 6 \text{ minutes per puzzle} \][/tex]

So, Maya takes 6 minutes to solve each puzzle.

#### 1.2. Calculating Amy's Puzzle Solving Rate
Amy takes 28 minutes to solve 4 puzzles.
Similarly, we find the rate in minutes per puzzle:

[tex]\[ \text{Amy's rate} = \frac{28 \text{ minutes}}{4 \text{ puzzles}} = 7 \text{ minutes per puzzle} \][/tex]

So, Amy takes 7 minutes to solve each puzzle.

### Part 2: Who Finishes First if They Had the Same Number of Puzzles?

#### 2.1. Hypothetical Scenario
Let’s assume Maya and Amy are both given the same number of puzzles to solve. For simplicity, let's say they both need to solve 20 puzzles.

#### 2.2. Time Taken by Maya to Solve 20 Puzzles
Using Maya's rate (6 minutes per puzzle):

[tex]\[ \text{Maya's total time} = 6 \text{ minutes/puzzle} \times 20 \text{ puzzles} = 120 \text{ minutes} \][/tex]

#### 2.3. Time Taken by Amy to Solve 20 Puzzles
Using Amy's rate (7 minutes per puzzle):

[tex]\[ \text{Amy's total time} = 7 \text{ minutes/puzzle} \times 20 \text{ puzzles} = 140 \text{ minutes} \][/tex]

#### 2.4. Conclusion
Comparing the total times:

[tex]\[ 120 \text{ minutes (Maya's time)} < 140 \text{ minutes (Amy's time)} \][/tex]

Therefore, Maya would finish first if they both had to solve the same number of puzzles.

### Part 3: Garden Hose Water Flow Rate

#### 3.1. Given Information
A garden hose supplies 36 gallons of water in 3 minutes.

#### 3.2. Gallons per Minute
We need to find the flow rate in gallons per minute. This is calculated by dividing the total gallons by the number of minutes:

[tex]\[ \text{Gallons per minute} = \frac{36 \text{ gallons}}{3 \text{ minutes}} = 12 \text{ gallons per minute} \][/tex]

So, the hose supplies water at a rate of 12 gallons per minute.

#### 3.3. Minutes per Gallon
We also need to find how many minutes it takes to supply one gallon of water:

[tex]\[ \text{Minutes per gallon} = \frac{3 \text{ minutes}}{36 \text{ gallons}} = \frac{1}{12} \text{ minutes per gallon} \approx 0.0833 \text{ minutes per gallon} \][/tex]

So, it takes approximately 0.0833 minutes (or [tex]\(\frac{1}{12}\)[/tex] of a minute) to supply one gallon of water.

### Summary of Solutions:

1. Maya's puzzle-solving rate: 6 minutes per puzzle
2. Amy's puzzle-solving rate: 7 minutes per puzzle
3. Maya finishes first when they solve the same number of puzzles.
4. Garden hose water flow rate:
- 12 gallons per minute
- 0.0833 minutes per gallon

This detailed analysis should clarify the rates and comparison as well as the water flow calculation!

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