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William recently started running after school. Yesterday, he ran 4.84.8 miles in 4141 minutes and 66 seconds. Today, he ran 4.14.1 miles in 3333 minutes and 44 seconds. What was William's average speed over the two runs?\newlineWrite 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 4.84.8 miles in 4141 minutes and 66 seconds. Today, he ran 4.14.1 miles in 3333 minutes and 44 seconds. What was William's average speed over the two runs?\newlineWrite your answer as a whole number, a decimal, or a simplified fraction or mixed number. Do not round.\newline\newline____ miles per minute\newline
  1. 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.\newlineFor the first run: 4141 minutes and 66 seconds can be converted to minutes by adding the seconds converted to minutes to the total minutes.\newline4141 minutes + (66 seconds \/ 6060 seconds/minute) = 4141 minutes + 0.10.1 minutes = 41.141.1 minutes.
  2. Calculate speed for first run: For the second run: 3333 minutes and 44 seconds can be converted to minutes in the same way.\newline3333 minutes + rac{4 \text{ seconds}}{60 \text{ seconds/minute}} = 33 minutes + 0.06670.0667 minutes ≈33.07\approx 33.07 minutes (rounded to two decimal places for ease of calculation).
  3. Calculate speed for second run: Now, we calculate the speed for each run using the formula Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}.\newline First run speed = 4.8 miles41.1 minutes\frac{4.8 \text{ miles}}{41.1 \text{ minutes}}.
  4. Calculate average speed: Perform the calculation for the first run speed.\newlineFirst run speed ≈4.8 miles41.1 minutes≈0.1168 miles per minute\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).
  5. Calculate average speed: Perform the calculation for the first run speed.\newlineFirst run speed ≈4.8\approx 4.8 miles ÷41.1\div 41.1 minutes ≈0.1168\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.\newlineSecond run speed = 4.14.1 miles ÷33.07\div 33.07 minutes.
  6. Calculate average speed: Perform the calculation for the first run speed.\newlineFirst run speed ≈4.8 miles41.1 minutes≈0.1168 miles per minute\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.\newlineSecond run speed =4.1 miles33.07 minutes= \frac{4.1 \text{ miles}}{33.07 \text{ minutes}}.Perform the calculation for the second run speed.\newlineSecond run speed ≈4.1 miles33.07 minutes≈0.1240 miles per minute\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).
  7. Calculate average speed: Perform the calculation for the first run speed.\newlineFirst run speed ≈4.8 miles41.1 minutes≈0.1168 miles per minute\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.\newlineSecond run speed =4.1 miles33.07 minutes= \frac{4.1 \text{ miles}}{33.07 \text{ minutes}}.Perform the calculation for the second run speed.\newlineSecond run speed ≈4.1 miles33.07 minutes≈0.1240 miles per minute\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 22.\newlineAverage speed =(First run speed+Second run speed)2= \frac{(\text{First run speed} + \text{Second run speed})}{2}.
  8. Calculate average speed: Perform the calculation for the first run speed.\newlineFirst run speed ≈4.8 miles41.1 minutes≈0.1168 miles per minute\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.\newlineSecond run speed =4.1 miles33.07 minutes= \frac{4.1 \text{ miles}}{33.07 \text{ minutes}}.Perform the calculation for the second run speed.\newlineSecond run speed ≈4.1 miles33.07 minutes≈0.1240 miles per minute\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 22.\newlineAverage speed =First run speed+Second run speed2= \frac{\text{First run speed} + \text{Second run speed}}{2}.Perform the calculation for the average speed.\newlineAverage speed ≈0.1168 miles per minute+0.1240 miles per minute2≈0.2408 miles per minute2≈0.1204 miles per minute\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}.

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