A cheetah

A cheetah was separated from his brothers on a hunting mission.  The brothers were at the watering hole 120 km away.  The lost cheetah knew that he had to make it back before sundown, which was 1.5 hours away.  His brothers had planned to leave the watering hole by sundown.  The cheetah plans to reach his brothers.  Beginning: For the first 40 km of the trip, the cheetah will run at 55% of his maximum speed.  Middle: For the next 50 km of the trip, the cheetah will run at 70% of his full speed.  End: For the final 30 km of the trip, the cheetah will run at his maximum speed.  Does the cheetah make it back to his brothers before they leave the pond?

Correct answer:

v =  80 km/h
v2 =  116.1039 km/h

Step-by-step explanation:

s=120 km t=1.5 h  v=s/t=120/1.5=80 km/h
t1= 40/(0.55 v2) t2= 50/(0.70 v2) t3= 30/v2  t=t1+t2+t3 40/(0.55 v2)  + 50/(0.70 v2) + 30/v2 = t  40/0.55+50/0.70+30=t v2 40/0.55+50/0.70+30=1.5 v2  1.5v2=174.155844  v2=1.5174.15584416=116.1038961  v2=778940116.103896=116.1039 km/h

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