Let's break down the problem step by step to find the missing expression that represents the distance Eduardo traveled on his trip home.
1. Understand the Given Data:
- The average speed on the way to work: [tex]\( 55 \)[/tex] miles per hour
- The average speed on the way home: [tex]\( 40 \)[/tex] miles per hour
- The total time for the round trip: [tex]\( 1.25 \)[/tex] hours
2. Define Variables:
- Let [tex]\( t \)[/tex] represent the time (in hours) for the commute to work.
- Therefore, the time for the commute home will be [tex]\( 1.25 - t \)[/tex].
3. Calculate Distance to Work:
- The distance to work is given by the formula: [tex]\(\text{Distance} = \text{Rate} \times \text{Time}\)[/tex]
- For the commute to work, the distance is: [tex]\( 55 \times t \)[/tex] miles.
4. Calculate Time and Distance for the Commute Home:
- The time for the commute home is [tex]\( 1.25 - t \)[/tex] hours.
- The rate for the commute home is [tex]\( 40 \)[/tex] miles per hour.
- The distance for the commute home is: [tex]\(\text{Distance} = \text{Rate} \times \text{Time}\)[/tex]
Therefore, the distance for the commute home is:
[tex]\[ \text{Distance} = 40 \times (1.25 - t) \][/tex]
So, the missing expression that represents the distance, in miles, for Eduardo's trip home is:
[tex]\[ 40(1.25 - t) \][/tex]
Hence, the correct expression to be filled in the table for the distance of the commute to home is:
[tex]\[ 40(1.25 - t) \][/tex]
- The correct option is:
[tex]\[ 40(1.25 - t) \][/tex]
