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:
Complete Question
"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.
If the cheetah sprinted at maximum speed, how far would the cheetah have traveled?
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.
b. Let t = 10 and solve for the distance the cheetah covered in 10 minutes.
Suppose the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes.
c. How far would the cheetah have traveled in the first 8 minutes? Show how you arrived at your answer.
d. How far would the cheetah have traveled in the next 8 minutes? Show how you arrived at your answer.
e. How much farther did the cheetah travel in the first 8 minutes than in the second 8 minutes?
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."
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.
