Part A
The instructions don't say the max speed, but we can find the max speed is 70 mph (since 1.75*40 = 70).
Convert that to miles per minute
70 mph = 70/60 = (7/6) miles per minute
In 8 minutes, the cheetah travels about (7/6)*8 = 9.333 miles at max speed.
Answer: Approximately 9.333 miles
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Part B
40 mph = (40/60) miles per minute
40 mph = (2/3) miles per minute
distance = rate*time
distance = (2/3)*8
distance = 5.333 miles approximately
Answer: Approximately 5.333 miles
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Part C
Subtract the results from parts A and B
9.333 - 5.333 = 4
The decimal portions cancel out completely since both have the '3's go on forever.
Answer: 4 miles
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Part D
d1 = distance traveled the first 8 minutes
d1 = (rate)*(time)
d1 = (1.75r)*(8)
d1 = 14r
where r is the speed in miles per minute traveled during the next 8 minutes
d2 = distance traveled the second 8 minute period
d2 = (rate)*(time)
d2 = r*8
d2 = 8r
Now divide the distances d1 over d2
d1/d2 = (14r)/(8r)
d1/d2 = 14/8
d1/d2 = 1.75
Answer: Yes the distance traveled during the first 8 minutes is 1.75 times greater compared to the distance traveled during the second 8 minutes.
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Part E
I'm assuming you meant to say "half" instead of "have".
The first leg of the round trip is 8+8 = 16 minutes.
The second leg, or return journey, of the trip is 16/2 = 8 minutes.
The total distance is d1+d2 = 14r+8r = 22r where r is r = 2/3 calculated back in part B
This means the total distance traveled is 22r = 22*(2/3) = 44/3 miles.
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Let's calculate the average speed on the first leg of the trip
d = r*t
44/3 = r*16
16r = 44/3
r = (44/3)*(1/16)
r = (44*1)/(3*16)
r = 44/48
r = 11/12
r = 0.917 miles per minute approximately
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Now let's calculate the return speed
d = r*t
44/3 = r*8
8r = 44/3
r = (44/3)*(1/8)
r = 44/24
r = 11/6
r = 1.833 miles per minute approximately
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Let's compare the results 11/12 and 11/6
We can see that 11/6 is twice as large compared to 11/12
Note that (11/12)*2 = 22/12 = 11/6
So if the cheetah goes from point A to point B in some amount of time, and goes from B to A in half the amount of time, then it must have traveled twice as fast to get back home.
A simple example could be as follows. Let's say a car travels 120 miles and does so for 4 hours. Its speed is 120/4 = 30 mph. Now let's say it comes back home and takes 2 hours (which is half of 4) so its speed is now 120/2 = 60 mph. The jump from 30 to 60 is times 2, showing the return speed is twice as fast to effectively counterbalance the fact we halved the time value.
Answer: The cheetah's average speed on the return trip is twice as fast compared to the average speed on the first leg of the trip.
Answer:Part B
40 mph = (40/60) miles per minute
40 mph = (2/3) miles per minute
distance = rate*time
distance = (2/3)*8
distance = 5.333 miles approximately
Answer: Approximately 5.333 miles
Step-by-step explanation:
