Question

the cheetah traveled 1.75 times faster for the first 8 minutes than it did for the second 8 minutes. was the distance traveled during the first 8 minutes 1.75 times greater than the distance traveled during the second 8 minutes? show the calculation to justify your answer.

Explanation:

Step1: Recall the distance formula

The formula for distance is \( d = v \times t \), where \( d \) is distance, \( v \) is velocity (speed), and \( t \) is time.

Step2: Define variables for speed and time

Let the speed of the cheetah in the second 8 minutes be \( v_2 \), so the speed in the first 8 minutes \( v_1=1.75v_2 \). The time for both intervals \( t_1 = t_2=8 \) minutes.

Step3: Calculate distance for first interval

Using the distance formula, distance in first 8 minutes \( d_1=v_1\times t_1 = 1.75v_2\times8 \).

Step4: Calculate distance for second interval

Distance in second 8 minutes \( d_2 = v_2\times t_2=v_2\times8 \).

Step5: Find the ratio of \( d_1 \) to \( d_2 \)

\( \frac{d_1}{d_2}=\frac{1.75v_2\times8}{v_2\times8} \). The \( v_2 \) and 8 terms cancel out, leaving \( \frac{d_1}{d_2} = 1.75 \), so \( d_1 = 1.75d_2 \).

Answer:

Yes, the distance traveled during the first 8 minutes is 1.75 times greater than the distance traveled during the second 8 minutes. The calculation shows that when taking the ratio of the distances \( \frac{d_1}{d_2}=\frac{1.75v_2\times8}{v_2\times8} = 1.75 \), so \( d_1 = 1.75d_2 \).