Are the following statements true?
32 m : 64 m = 6 sec : 12 sec

Answer

To determine if the statement \( 32 \, \text{m} : 64 \, \text{m} = 6 \, \text{sec} : 12 \, \text{sec} \) is true, we will compare the two ratios step by step.

### Step 1: Write the Ratios as Fractions
Convert both ratios into fractions.

- For the left-hand side (LHS):
\[ \frac{32 \, \text{m}}{64 \, \text{m}} \]

- For the right-hand side (RHS):
\[ \frac{6 \, \text{sec}}{12 \, \text{sec}} \]

### Step 2: Simplify the Fractions
Now, we will simplify both fractions.

- Simplifying the LHS:
\[ \frac{32}{64} = \frac{1}{2} \]
(since \( 32 \times 2 = 64 \))

- Simplifying the RHS:
\[ \frac{6}{12} = \frac{1}{2} \]
(since \( 6 \times 2 = 12 \))

### Step 3: Compare the Simplified Fractions
Now we compare the simplified fractions from both sides.

- LHS: \( \frac{1}{2} \)
- RHS: \( \frac{1}{2} \)

Since both fractions are equal, we can conclude that:

\[ 32 \, \text{m} : 64 \, \text{m} = 6 \, \text{sec} : 12 \, \text{sec} \]

### Conclusion
The statement is **true**.

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