Let's go through the problem step by step in order to find the correct expression that represents the distance for the commute home.
1. Identify the given values:
- Rate of commute to work: [tex]\( 55 \)[/tex] miles per hour
- Round trip time: [tex]\( 1.25 \)[/tex] hours
- Rate of commute home: [tex]\( 40 \)[/tex] miles per hour
2. Determine the total distance commuted:
- Since the rate of commute to work is [tex]\( 55 \)[/tex] mph, and if [tex]\( t \)[/tex] represents the time taken to commute to work, the expression for the distance commuted to work is [tex]\( 55t \)[/tex] miles.
3. Relate the times with the total time:
- The total round trip time is [tex]\( 1.25 \)[/tex] hours. Therefore, if the time taken to commute to work is [tex]\( t \)[/tex], the time taken to commute back home is [tex]\( 1.25 - t \)[/tex].
4. Find the expression for the distance commuted home:
- The distance for the commute home is given by the rate multiplied by the time. So we use the rate of commute home, [tex]\( 40 \)[/tex] mph, and time taken to commute home, [tex]\( 1.25 - t \)[/tex].
- Therefore, the expression for the distance of the commute home is [tex]\( 40 \times (1.25 - t) \)[/tex].
To summarize, the correct expression for the distance in miles for the trip home is: [tex]\( 40 (1.25 - t) \)[/tex].
