Question in the attachment

[eitijan]

IMO E

[OptimusPrep]

Given: Assume the total distance to be 100x feet
1. Ryan swims 25x at full speed
2. Ryan swims (3/4)*75x = 56.25x at a reduced speed
3. Ryan swims 18.75x at full speed

Required: Average speed during the race.
This can be calculated if we have the total distance and the total time taken

Statement 1: Total distance = 100 feet
This does not tell us anything about the time.
Insufficient

Statement 2: Reduced speed = 1/3 of the full speed
Assume full speed = 3s
Reduced speed = s

Total distance = 100x
Total time taken = 25x/3s + 56.25x/s + 18.75x/3s

Average speed = 100x / (25x/3s + 56.25x/s + 18.75x/3s)
We cannot solve for average speed
Insufficient

Combining both the statements:
Average speed = 100 / (25/3s + 56.25/s + 18.75/3s)
Still we cannot calculate the average speed.
Insufficient

Option E

[GMATGuruNY]

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.