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Answer:
a. D = 1.167t miles per minute
b. 11.67 miles
c. 9.33 miles
d. 5.33 miles
e. 4 miles
f. Therefore, the distance traveled by the cheetah during the first 8 minutes is 1.75 times greater than the distance traveled during the second 8 minutes.
Step-by-step explanation:
<u>Complete Question</u>
<em>"A cheetah sitting under a tree sprints toward its prey at 70 mph. It runs back to its initial spot by the tree at a modest 40 mph. The cheetah has embarked on a round-trip. Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph.</em>
<em>If the cheetah sprinted at maximum speed, how far would the cheetah have traveled? </em>
<em>a. Set up an equation to represent the distance the cheetah covered in terms of t minutes running at maximum speed. Remember, units of distance and time must agree. Use the conversion information from the warm-up to write a rate in miles per minute.</em>
<em> </em>
<em>b. Let t = 10 and solve for the distance the cheetah covered in 10 minutes. </em>
<em> </em>
<em>Suppose the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes. </em>
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<em>c. How far would the cheetah have traveled in the first 8 minutes? Show how you arrived at your answer. </em>
<em> </em>
<em>d. How far would the cheetah have traveled in the next 8 minutes? Show how you arrived at your answer. </em>
<em> </em>
<em>e. How much farther did the cheetah travel in the first 8 minutes than in the second 8 minutes? </em>
<em> </em>
<em>f. 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."</em>
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Solution:
a.
The distance equation is D = RT, where
D is distance
R is rate (speed)
T is time
If cheetah travels at max speed, 70 mph, we can say D = 70t
There are 60 minutes in 1 hours, so the distance in miles per minute is:
D = 1.167t miles per minute
b.
Given t = 10 minutes, the distance covered using formula would be
D = RT
D = 1.167 * 10 = 11.67 miles
c.
Since Cheetah traveled at max speed (70mph) for the first leg of 8 minutes, the distance covered would be:
D = RT
D = 1.167 * 8
D = 9.33 miles
d.
Next leg of 8 minutes would be at 40mph, to get that in minutes, we divide by 60, so rate would be 40/60. Hence, distance covered is:
D = RT
D = (40/60) * 8 = 5.33 miles
e.
The distance traveled in first 8 minutes is 9.33
The distance traveled in second 8 minutes is 5.33,
Hence, the more distance is 9.33 - 5.33 = 4 miles
f.
To justify if 9.33 is actually 1.75 times that of 5.33, we multiply 5.33 by 1.75 and see if it is 9.33. So
1.75 * 5.33 = 9.33 [in fact, it is!]
Therefore, the distance traveled by the cheetah during the first 8 minutes is 1.75 times greater than the distance traveled during the second 8 minutes.