Travelled at full speed are 1/4 of the total distance and then 1/4 of the remaining distance.
To determine the fraction traveled at full speed, let the total distance = 16 feet.
Initial distance traveled at full speed = (1/4)(16) = 4 feet.
Total remaining distance = 16-14 = 12 feet.
Remaining distance traveled at full speed = (1/4)(12) = 3 feet.
Total distance traveled at full speed = 4+3 = 7 feet.
Thus:
7/16 of the total distance is traveled at full speed, implying that 9/16 of the total distance is traveled at the lower speed.
Statements combined:
Case 1: full speed = 3 feet per hour, lower speed = 1 foot per hour
At 3 feet per hour, the time to travel 7/16 of the 100 feet = d/r = [(7/16)(100)]/3.
At 1 foot per hour, the time to travel 9/16 of the 100 feet = d/r = [(9/16)(100)]/1 = (9/16)(100).
Total time = [(7/16)(100)]3 + (9/16)(100).
Case 2: full speed = 300 feet per hour, lower speed = 100 feet per hour
At 300 feet per hour, the time to travel 7/16 of the 100 feet = d/r = [(7/16)(100)]/300 = (7/16)/3.
At 100 feet per hour, the time to travel 9/16 of the 100 feet = d/r = [(9/16)(100)]/100 = 9/16.
Total time = (7/16)/3 + 9/16.
Since the total time in Case 1 is different from the total time in Case 2, each case will yield a DIFFERENT AVERAGE SPEED.
Since the average speed for the whole race can be different values, INSUFFICIENT.
The correct answer is E.
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