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Eduardo's average speed on his commute to work was 55 miles per hour. On the way home, he hit traffic and only averaged 40 miles per hour. If the round trip took him 1.25 hours, which expression represents the distance, in miles, for his trip home that is missing from the table?

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& \text{Rate (mi/h)} & \text{Time (h)} & \text{Distance (miles)} \\
\hline
\text{Commute to Work} & 55 & $t$ & $55t$ \\
\hline
\text{Commute to Home} & 40 & & ? \\
\hline
\end{tabular}
\][/tex]

A. [tex]$t - 1.25$[/tex]

B. [tex]$1.25 - t$[/tex]

C. [tex]$40(1.25 - t)$[/tex]

D. [tex]$40(t - 1.25)$[/tex]

Sagot :

GinnyAnswer
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]
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