9. a woman runs three miles in 24 minutes.
a. find the average speed of the woman in miles per minute.
b. if one mile is 1609 meters, find the woman’s average speed in meters per second.

10. the white fir tree grows an average of sixteen inches per year.
a. find the average speed of the tree in inches per year.
b. convert your answer from $\frac{\text{in}}{\text{year}}$ to $\frac{\text{in}}{\text{day}}$. write your answer in scientific notation.
c. convert your answer from $\frac{\text{in}}{\text{day}}$ to $\frac{\text{m}}{\text{hr}}$. write your answer in scientific notation.

Question

9. a woman runs three miles in 24 minutes.
   a. find the average speed of the woman in miles per minute.
   b. if one mile is 1609 meters, find the woman’s average speed in meters per second.

10. the white fir tree grows an average of sixteen inches per year.
    a. find the average speed of the tree in inches per year.
    b. convert your answer from $\frac{\text{in}}{\text{year}}$ to $\frac{\text{in}}{\text{day}}$. write your answer in scientific notation.
    c. convert your answer from $\frac{\text{in}}{\text{day}}$ to $\frac{\text{m}}{\text{hr}}$. write your answer in scientific notation.

Accepted Answer

### Problem 9a
# Explanation:
## Step1: Recall speed formula
Speed is defined as distance divided by time, so $ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $.
## Step2: Substitute values
The distance is 3 miles and the time is 24 minutes. So, $ \text{Speed} = \frac{3}{24} $ miles per minute.
## Step3: Simplify the fraction
$ \frac{3}{24} = \frac{1}{8} = 0.125 $ miles per minute.
# Answer:
0.125 miles per minute

### Problem 9b
# Explanation:
## Step1: Convert miles to meters
From part 9a, the speed is 0.125 miles per minute. Since 1 mile = 1609 meters, multiply by 1609: $ 0.125 \times 1609 = 201.125 $ meters per minute.
## Step2: Convert minutes to seconds
There are 60 seconds in a minute, so divide by 60: $ \frac{201.125}{60} \approx 3.352 $ meters per second.
# Answer:
Approximately 3.35 meters per second (or more precisely $ \frac{201.125}{60} \approx 3.352 $ m/s)

### Problem 10a
# Explanation:
## Step1: Identify given values
The tree grows 16 inches per year, so the average speed in inches per year is directly given.
# Answer:
16 inches per year

### Problem 10b
# Explanation:
## Step1: Recall conversion factor
There are 365 days in a year (assuming non - leap year). To convert from inches per year to inches per day, divide the speed in inches per year by the number of days in a year.
## Step2: Perform the calculation
$ \frac{16}{365} \approx 0.0438356 $ inches per day. In scientific notation, this is $ 4.38356\times 10^{-2} $ inches per day (or more precisely, $ \frac{16}{365}=\frac{16}{3.65\times 10^{2}}\approx 4.38356\times 10^{-2} $ in/day).
# Answer:
$ 4.38\times 10^{-2} $ inches per day (or more accurate $ 4.38356\times 10^{-2} $ in/day)

### Problem 10c
# Explanation:
## Step1: Convert inches to meters
We know that 1 inch = 0.0254 meters. From part 10b, the speed is $ \frac{16}{365} $ in/day. Multiply by 0.0254 to get meters per day: $ \frac{16}{365}\times0.0254=\frac{16\times0.0254}{365}=\frac{0.4064}{365}\approx 0.0011134 $ meters per day.
## Step2: Convert days to hours
There are 24 hours in a day, so divide by 24 to get meters per hour: $ \frac{0.0011134}{24}\approx 4.639\times 10^{-5} $ meters per hour.
(Alternatively, using scientific notation throughout:
First, $ 16\space in/year = 16\space in/(365\space day)= \frac{16}{365}\space in/day\approx 4.38356\times 10^{-2}\space in/day $
Convert inches to meters: $ 4.38356\times 10^{-2}\space in/day\times0.0254\space m/in = 4.38356\times 2.54\times 10^{-4}\space m/day\approx 1.1134\times 10^{-3}\space m/day $
Convert days to hours: $ \frac{1.1134\times 10^{-3}\space m/day}{24\space hr/day}\approx 4.639\times 10^{-5}\space m/hr $)
# Answer:
$ 4.64\times 10^{-5} $ meters per hour (or more accurate $ 4.639\times 10^{-5} $ m/hr)

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QUESTION IMAGE

Question

Explanation:

Problem 9a

Step1: Recall speed formula

Step2: Substitute values

Step3: Simplify the fraction

Step1: Convert miles to meters

Step2: Convert minutes to seconds

Step1: Identify given values

Answer:

Problem 9b