Final answer:
The correct statements about the swimmer's average times and speeds are (a) the average time is 87 seconds and (d) the average speed is 1.15 m/s. Statement (a) correctly uses arithmetic mean for time, and (d) accurately calculates the arithmetic mean for speed.
Step-by-step explanation:
The student has recorded times of 90 seconds, 83 seconds, and 88 seconds, for a 100m freestyle race, corresponding to speeds of 1.11 m/s, 1.20 m/s, and 1.14 m/s respectively. To determine which statements are correct regarding average time and average speed, one must apply the correct formulas for these calculations.
a. The average time is 87 seconds, since (90+83+88)/3 = 87: This is the most straightforward way to calculate average time and is correct.
b. The average speed is 1.149 seconds: This is incorrect, as the formula used is not a proper method to calculate average speed; instead, it incorrectly calculates the harmonic mean of the speeds.
c. The average time is 86.9 seconds since 3/(1/90+1/83+1/88)=86.9: This calculation is indeed the harmonic mean of the times and not the arithmetic mean.
d. The average speed is 1.15 m/s since (1.11 + 1.20 + 1.14)/3 = 1.15: This is the correct way to calculate average speed and is a correct statement.
e. The average speed is 1.149 m/s since (1.11 x 1.2 x 1.14)^(1/3)=1.149: This formula is used to find the geometric mean of speeds, not the arithmetic mean, so this is incorrect for calculating the average speed.
f. The average time is 86.9 since (90 x 83 x 88)^(1/3)=86.9: This represents the geometric mean of the times, which is not the correct method to calculate average time.