$12$ . Ken's average speed for a trip is $14$ miles per hour. During the first part of the trip, he traveled at $15$ miles per hour for $2$ hours, and then traveled at a different speed for $1$ hour the rest of the way. What was her speed for the second part of the trip? $\newline$ E. $\quad 7.5 \mathrm{mph}$ $\newline$ F. $12.0 \mathrm{mph}$ $\newline$ G. $15.0 \mathrm{mph}$ $\newline$ H. $22.5 \mathrm{mph}$

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Add and subtract decimals: word problems

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12

. Ken's average speed for a trip is

14

miles per hour. During the first part of the trip, he traveled at

15

miles per hour for

2

hours, and then traveled at a different speed for

1

hour the rest of the way. What was her speed for the second part of the trip?

\newline

\quad 7.5 \mathrm{mph}

\newline

12.0 \mathrm{mph}

\newline

15.0 \mathrm{mph}

\newline

22.5 \mathrm{mph}

Calculate Total Distance: First, let's calculate the total distance Ken traveled during the first part of the trip at $15$ miles per hour for $2$ hours. $\newline$ Distance $=$ Speed $\times$ Time $\newline$ Distance $=$ $15$ mph $\times$ $2$ hours $\newline$ Distance $=$ $30$ miles
Find Total Distance: Next, we need to find out the total distance Ken traveled for the entire trip using his average speed and the total time. $\newline$ Ken's average speed is $14$ miles per hour for the entire trip, which lasted $3$ hours ( $2$ hours at the first speed and $1$ hour at the second speed). $\newline$ Total Distance = Average Speed $\times$ Total Time $\newline$ Total Distance = $14$ mph $\times$ $3$ hours $\newline$ Total Distance = $42$ miles
Calculate Distance Difference: Now, we subtract the distance Ken traveled during the first part of the trip from the total distance to find out how far he traveled during the second part of the trip. $\newline$ Distance during the second part = Total Distance - Distance during the first part $\newline$ Distance during the second part = $42$ miles - $30$ miles $\newline$ Distance during the second part = $12$ miles
Calculate Speed: Finally, we calculate Ken's speed during the second part of the trip. He traveled $12$ miles in $1$ hour. $\newline$ Speed during the second part $= \frac{\text{Distance during the second part}}{\text{Time during the second part}}$ $\newline$ Speed during the second part $= \frac{12 \text{ miles}}{1 \text{ hour}}$ $\newline$ Speed during the second part $= 12.0$ mph