Noah eats 1/3 of an apple in 1/6 of a minute. How much time will it take him to eat a full apple?

To determine how much time it will take Noah to eat a full apple, we can use a proportional reasoning approach.

### Step 1: Set up the proportion
Noah eats \( \frac{1}{3} \) of an apple in \( \frac{1}{6} \) of a minute. Therefore, we can write the relationship:

\[
\frac{1}{3} \text{ apple} = \frac{1}{6} \text{ minute}
\]

We want to find out how long it will take to eat \( 1 \) full apple. Let the time it takes to eat the full apple be \( t \).

\[
1 \text{ apple} = t \text{ minutes}
\]

### Step 2: Set up the equation

We can set up a proportion between the amount of apple eaten and the time spent eating:

\[
\frac{1}{3} \text{ apple} : \frac{1}{6} \text{ minute} = 1 \text{ apple} : t \text{ minutes}
\]

This gives the equation:

\[
\frac{1}{3} \div 1 = \frac{1}{6} \div t
\]

### Step 3: Solve for \( t \)

To solve for \( t \), cross-multiply:

\[
t = \left(1 \times \frac{1}{6}\right) \div \frac{1}{3}
\]

This simplifies to:

\[
t = \frac{1}{6} \times \frac{3}{1} = \frac{3}{6} = \frac{1}{2} \text{ minute}
\]

### Conclusion:
It will take Noah **\( \frac{1}{2} \) minute** (or 30 seconds) to eat a full apple.

Would you like any further details on this, or have any questions?

Here are 5 related questions:
1. What if Noah ate \( \frac{1}{4} \) of the apple in \( \frac{1}{8} \) of a minute?
2. How much of the apple would he eat in 1 minute?
3. If Noah ate 2 apples at the same rate, how much time would it take?
4. How much time would it take to eat half an apple?
5. What if Noah ate 1 apple in 1 minute—how fast is he compared to the original scenario?

**Tip:** To solve problems involving ratios, setting up proportions is an effective method.

Learn how to solve a problem where Noah eats 1/3 of an apple in 1/6 of a minute using proportions and fractions. This detailed solution is suitable for students in Grades 5-7 and covers proportional reasoning, including the use of ratios and fractions.

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