Answer:
1231 km/h
Step-by-step explanation:
The average speed is given by ...
average speed = (total distance)/(total time)
The total time will be the sum of times down and back, each of which is given by ...
time = distance/speed
Going to Mexico, the time required was ...
time down = (2000 km)/(1600 km/h) = 1.25 h
Coming back, the time required was ...
time back = (2000 km)/(1000 km/h) = 2.00 h
Then the average speed is ...
average speed = (2000 km + 2000 km)/(1.25 h +2.00 h) = 4000/3.25 km/h
≈ 1231 km/h
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Comment on average speed
The value we computed was ...
2/(1/s1 + 1/s2) . . . . where s1 and s2 are the speeds over the same distance
This is the harmonic mean of two numbers (the two speeds). The harmonic mean of n numbers is ...
harmonic mean = n/(1/a1 +1/a2 +1/a3 + ... + 1/an)
This mean generally finds less use than the typical arithmetic mean or geometric mean.
arithmetic mean = (a1 + a2 + a3 + ... + an)/n
geometric mean = (a1·a2·a3·...·an)^(1/n)
