Question

Choose the three proportions with solutions that solve for x.

6 days = x seconds

Question 2 options:

Solve for x.




Set up the proportion with the unit ratio.




Find number of minutes in 1 week.

Answer 1

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:

1. Convert days to hours:
\[ 6 \text{ days} = 6 \times 24 \text{ hours} = 144 \text{ hours} \]

2. Convert hours to minutes:
\[ 144 \text{ hours} = 144 \times 60 \text{ minutes} = 8640 \text{ minutes} \]

3. 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:
1. \( 6 \text{ days} = x \text{ seconds} \) where \( x = 518400 \) seconds.
2. Unit ratio: \( \frac{6 \text{ days}}{518400 \text{ seconds}} = \frac{1 \text{ day}}{86400 \text{ seconds}} \)
3. 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.