Are the following statements true?
45 km : 60 km = 12 hours : 15 hours

Answer

To determine if the statements \( 45 \text{ km} : 60 \text{ km} = 12 \text{ hours} : 15 \text{ hours} \) are true, we will simplify both ratios and compare them.

### Step 1: Simplify the Left-Hand Side (LHS)

The LHS is \( 45 \text{ km} : 60 \text{ km} \).

1. Write it as a fraction:
\[ \frac{45}{60} \]

2. Simplify the fraction:
- Find the greatest common divisor (GCD) of 45 and 60. The GCD is 15.
- Divide both the numerator and the denominator by 15:
\[ \frac{45 \div 15}{60 \div 15} = \frac{3}{4} \]

So, the simplified form of the LHS is \( \frac{3}{4} \).

### Step 2: Simplify the Right-Hand Side (RHS)

The RHS is \( 12 \text{ hours} : 15 \text{ hours} \).

1. Write it as a fraction:
\[ \frac{12}{15} \]

2. Simplify the fraction:
- Find the GCD of 12 and 15. The GCD is 3.
- Divide both the numerator and the denominator by 3:
\[ \frac{12 \div 3}{15 \div 3} = \frac{4}{5} \]

So, the simplified form of the RHS is \( \frac{4}{5} \).

### Step 3: Compare the Two Ratios

Now we have:
- LHS: \( \frac{3}{4} \)
- RHS: \( \frac{4}{5} \)

Since \( \frac{3}{4} \) is not equal to \( \frac{4}{5} \), we conclude that:

### Conclusion

The statement \( 45 \text{ km} : 60 \text{ km} = 12 \text{ hours} : 15 \text{ hours} \) is **false**.

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