To solve the problem of converting 6 days to seconds, we can follow these steps:
Step 1: Understand the Relationships
1 day has:
- 24 hours 1 hour has:
- 60 minutes 1 minute has:
- 60 seconds
Step 2: Set Up the Conversion
We can set up a conversion from days to seconds using the following relationships:
1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds
Step 3: Solve for x
We need to find the number of seconds in 6 days:
\[ 6 \text{ days} = x \text{ seconds} \] Using the conversion factors, we calculate as follows:
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Convert days to hours: \[ 6 \text{ days} = 6 \times 24 \text{ hours} = 144 \text{ hours} \]
-
Convert hours to minutes: \[ 144 \text{ hours} = 144 \times 60 \text{ minutes} = 8640 \text{ minutes} \]
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Convert minutes to seconds: \[ 8640 \text{ minutes} = 8640 \times 60 \text{ seconds} = 518400 \text{ seconds} \]
So, \( x = 518400 \) seconds.
Step 4: Set Up the Proportion with the Unit Ratio
The unit ratio for the conversion can be set up like this:
\[ \frac{6 \text{ days}}{x \text{ seconds}} = \frac{1 \text{ day}}{86400 \text{ seconds}} \]
Where: \[ 86400 \text{ seconds} = 24 \times 60 \times 60 \]
Step 5: Find the Number of Minutes in 1 Week
Next, to find the number of minutes in 1 week:
1 week = 7 days 1 day = 1440 minutes (since 1 day = 24 hours and 1 hour = 60 minutes)
Now, calculate: \[ 1 \text{ week} = 7 \text{ days} \times 1440 \text{ minutes/day} = 10080 \text{ minutes} \]
Summary of Proportions
The three proportions to consider are:
- \( 6 \text{ days} = x \text{ seconds} \) where \( x = 518400 \) seconds.
- Unit ratio: \( \frac{6 \text{ days}}{518400 \text{ seconds}} = \frac{1 \text{ day}}{86400 \text{ seconds}} \)
- Number of minutes in 1 week: \( 7 \text{ days} \times 1440 \text{ minutes/day} = 10080 \text{ minutes} \)
These proportions represent the solutions needed to answer your query.
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