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Max and Angela are both long-distance runners, but Angela runs more than Max. For every hour that Max spends running, Angela spends an hour and a half. Write a ratio that compares the time that Max spends running to the time that Angela spends running.

A. [tex]\(1: 1 \frac{1}{2}\)[/tex]

B. [tex]\(\frac{2}{3}\)[/tex]

C. [tex]\(1 \frac{1}{2}: 1\)[/tex]

D. [tex]\(1 \frac{1}{2}\)[/tex]


Sagot :

To solve the problem of comparing the time that Max spends running to the time that Angela spends running, we can use the information given:

- Max spends 1 hour running.
- Angela spends 1.5 hours running.

First, let's clarify the given options, since we aim to compare Max's running time to Angela's running time.

### Step-by-Step Solution

1. Identify the times spent running:
- Max's running time: 1 hour
- Angela's running time: 1.5 hours

2. Write the times as fractions or decimal values:
- Max: 1 (which is 1.0 in decimal form)
- Angela: 1.5 (which is [tex]\( \frac{3}{2} \)[/tex] in fraction form)

3. Calculate the ratio:
The ratio comparing Max's running time to Angela's running time is calculated by dividing Max's time by Angela's time:

[tex]\[ \text{Ratio} = \frac{\text{Max's time}}{\text{Angela's time}} = \frac{1}{1.5} \][/tex]

4. Simplify the ratio:
To simplify [tex]\(\frac{1}{1.5}\)[/tex], divide both the numerator and the denominator by 1.5:

[tex]\[ \frac{1}{1.5} = \frac{1 \div 1.5}{1.5 \div 1.5} = \frac{1}{1.5} = \frac{1}{1 \frac{1}{2}} = \frac{2}{3} \][/tex]

Thus, the simplified ratio of the time Max spends running to the time Angela spends running is [tex]\(\frac{2}{3}\)[/tex].

### Conclusion:
The correct ratio comparing the time Max spends running to the time Angela spends running is:

[tex]\[ \boxed{\frac{2}{3}} \][/tex]