To solve the proportion \( 6 \text{ days} = x \text{ seconds} \), we first need to convert days into seconds. We know that:
- 1 day = 24 hours
- 1 hour = 60 minutes
- 1 minute = 60 seconds
So, the total number of seconds in 6 days can be calculated as follows:
\[ 6 \text{ days} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} \]
Now, let's calculate it step-by-step:
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Calculate the number of hours in 6 days: \[ 6 \text{ days} \times 24 \text{ hours/day} = 144 \text{ hours} \]
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Calculate the number of minutes in 144 hours: \[ 144 \text{ hours} \times 60 \text{ minutes/hour} = 8640 \text{ minutes} \]
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Calculate the number of seconds in 8640 minutes: \[ 8640 \text{ minutes} \times 60 \text{ seconds/minute} = 518400 \text{ seconds} \]
Thus, \( x = 518400 \text{ seconds} \).
To express this as three different proportions that can solve for \( x \), we can create the following three equivalent proportions:
- \(\frac{6 \text{ days}}{x \text{ seconds}} = \frac{1 \text{ day}}{86400 \text{ seconds}}\)
- \(\frac{6 \text{ days}}{x \text{ seconds}} = \frac{1 \text{ hour}}{3600 \text{ seconds}}\)
- \(\frac{6 \text{ days}}{x \text{ seconds}} = \frac{1 \text{ minute}}{60 \text{ seconds}}\)
Each of these proportions can be used to solve for \( x \) in the same way we calculated it originally.