William recently started running after school. Yesterday, he ran $4.8$ miles in $41$ minutes and $6$ seconds. Today, he ran $4.1$ miles in $33$ minutes and $4$ seconds. What was William's average speed over the two runs? $\newline$ Write your answer as a whole number, a decimal, or a simplified fraction or mixed number. Do not round. $\newline$ $\newline$ ____ miles per minute $\newline$

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Q. William recently started running after school. Yesterday, he ran

4.8

miles in

41

minutes and

6

seconds. Today, he ran

4.1

miles in

33

minutes and

4

seconds. What was William's average speed over the two runs?

\newline

Write your answer as a whole number, a decimal, or a simplified fraction or mixed number. Do not round.

\newline

\newline

____ miles per minute

\newline

Convert time to minutes: First, we need to convert the time for each run from minutes and seconds to just minutes to make the calculations easier. $\newline$ For the first run: $41$ minutes and $6$ seconds can be converted to minutes by adding the seconds converted to minutes to the total minutes. $\newline$ $41$ minutes + ( $6$ seconds \/ $60$ seconds/minute) = $41$ minutes + $0.1$ minutes = $41.1$ minutes.
Calculate speed for first run: For the second run: $33$ minutes and $4$ seconds can be converted to minutes in the same way. $\newline$ $33$ minutes + rac{4 \text{ seconds}}{60 \text{ seconds/minute}} = 33 minutes + $0.0667$ minutes $\approx 33.07$ minutes (rounded to two decimal places for ease of calculation).
Calculate speed for second run: Now, we calculate the speed for each run using the formula $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ . $\newline$ First run speed = $\frac{4.8 \text{ miles}}{41.1 \text{ minutes}}$ .
Calculate average speed: Perform the calculation for the first run speed. $\newline$ First run speed $\approx \frac{4.8 \text{ miles}}{41.1 \text{ minutes}} \approx 0.1168 \text{ miles per minute}$ (rounded to four decimal places for precision in the final average).
Calculate average speed: Perform the calculation for the first run speed. $\newline$ First run speed $\approx 4.8$ miles $\div 41.1$ minutes $\approx 0.1168$ miles per minute (rounded to four decimal places for precision in the final average).Next, calculate the speed for the second run using the same formula. $\newline$ Second run speed = $4.1$ miles $\div 33.07$ minutes.
Calculate average speed: Perform the calculation for the first run speed. $\newline$ First run speed $\approx \frac{4.8 \text{ miles}}{41.1 \text{ minutes}} \approx 0.1168 \text{ miles per minute}$ (rounded to four decimal places for precision in the final average).Next, calculate the speed for the second run using the same formula. $\newline$ Second run speed $= \frac{4.1 \text{ miles}}{33.07 \text{ minutes}}$ .Perform the calculation for the second run speed. $\newline$ Second run speed $\approx \frac{4.1 \text{ miles}}{33.07 \text{ minutes}} \approx 0.1240 \text{ miles per minute}$ (rounded to four decimal places for precision in the final average).
Calculate average speed: Perform the calculation for the first run speed. $\newline$ First run speed $\approx \frac{4.8 \text{ miles}}{41.1 \text{ minutes}} \approx 0.1168 \text{ miles per minute}$ (rounded to four decimal places for precision in the final average).Next, calculate the speed for the second run using the same formula. $\newline$ Second run speed $= \frac{4.1 \text{ miles}}{33.07 \text{ minutes}}$ .Perform the calculation for the second run speed. $\newline$ Second run speed $\approx \frac{4.1 \text{ miles}}{33.07 \text{ minutes}} \approx 0.1240 \text{ miles per minute}$ (rounded to four decimal places for precision in the final average).Finally, calculate the average speed over the two runs by taking the sum of the speeds and dividing by $2$ . $\newline$ Average speed $= \frac{(\text{First run speed} + \text{Second run speed})}{2}$ .
Calculate average speed: Perform the calculation for the first run speed. $\newline$ First run speed $\approx \frac{4.8 \text{ miles}}{41.1 \text{ minutes}} \approx 0.1168 \text{ miles per minute}$ (rounded to four decimal places for precision in the final average).Next, calculate the speed for the second run using the same formula. $\newline$ Second run speed $= \frac{4.1 \text{ miles}}{33.07 \text{ minutes}}$ .Perform the calculation for the second run speed. $\newline$ Second run speed $\approx \frac{4.1 \text{ miles}}{33.07 \text{ minutes}} \approx 0.1240 \text{ miles per minute}$ (rounded to four decimal places for precision in the final average).Finally, calculate the average speed over the two runs by taking the sum of the speeds and dividing by $2$ . $\newline$ Average speed $= \frac{\text{First run speed} + \text{Second run speed}}{2}$ .Perform the calculation for the average speed. $\newline$ Average speed $\approx \frac{0.1168 \text{ miles per minute} + 0.1240 \text{ miles per minute}}{2} \approx \frac{0.2408 \text{ miles per minute}}{2} \approx 0.1204 \text{ miles per minute}$ .