Question

question 5
if john, travelling at a constant speed on a stretch of highway, covers 25 miles in 30 minutes, how far does he travel in 3 hours at the same rate of speed?

question 6
a ranger tags 100 rabbits in a forest, then waits a few days so they spread evenly throughout the forest. he then captures 20 rabbits and notices that three have tags on them. about how many rabbits are in the forest?

Explanation:

Question 5

Step 1: Convert 3 hours to minutes

Since 1 hour = 60 minutes, 3 hours = \( 3\times60 = 180 \) minutes.

Step 2: Find the number of 30 - minute intervals in 180 minutes

The number of 30 - minute intervals is \( \frac{180}{30}=6 \).

Step 3: Calculate the distance traveled in 3 hours

John travels 25 miles in 30 minutes. So in 6 intervals of 30 minutes (which is 3 hours), the distance traveled is \( 25\times6 = 150 \) miles.

We can use the proportion method for estimating the population. Let the total number of rabbits in the forest be \( N \). The proportion of tagged rabbits in the second sample should be approximately equal to the proportion of tagged rabbits in the entire population.
The number of tagged rabbits is 100, the size of the second sample is 20, and the number of tagged rabbits in the second sample is 3. So we set up the proportion:
\( \frac{\text{Number of tagged rabbits}}{\text{Total number of rabbits}}=\frac{\text{Number of tagged rabbits in the second sample}}{\text{Size of the second sample}} \)
\( \frac{100}{N}=\frac{3}{20} \)

Step 1: Cross - multiply

Cross - multiplying gives us \( 3N=100\times20 \).

Step 2: Solve for N

\( 3N = 2000 \), then \( N=\frac{2000}{3}\approx667 \) (rounded to the nearest whole number).

Answer:

150 miles

Question 6 (assuming the missing part is "and notices that three have tags on them. About how many rabbits are in the forest?")