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If a person averaged 40 miles per hour on their trip home and the round trip took 1.25 hours, which expression represents the distance, in miles, for the trip home?

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

GinnyAnsweridn
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].
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