Question

1. triathlon you compete in a triathlon that consists of a $\frac{1}{4}$ mile swim, a 9 mile bike ride, and a 3 mile run. you complete the swim in 8 minutes, the bike ride in 24 minutes, and the run in 19 minutes. which part did you finish with a faster average speed? why can you estimate to answer the question?
2. home videos for the 5 year period from 1995 through 1999, the average american watched 256 hours of home videos. find the average number of hours watched per year.

source: veronis, suhler, & associates

Explanation:

For Question 12:

Step1: Calculate swim speed

Average speed = distance/time. Swim distance: $\frac{1}{4}$ mile, time: 8 min.
$\text{Swim speed} = \frac{\frac{1}{4}}{8} = \frac{1}{32} = 0.03125$ miles per minute

Step2: Calculate bike speed

Bike distance: 9 miles, time:24 min.
$\text{Bike speed} = \frac{9}{24} = 0.375$ miles per minute

Step3: Calculate run speed

Run distance:3 miles, time:19 min.
$\text{Run speed} = \frac{3}{19} \approx 0.1579$ miles per minute

Step4: Compare speeds

Compare 0.03125, 0.375, 0.1579.
$0.375 > 0.1579 > 0.03125$

Step1: Divide total by years

Total hours:256, number of years:5.
$\text{Average per year} = \frac{256}{5}$

Step2: Compute the value

$\frac{256}{5} = 51.2$

Answer:

You finished the bike ride with the fastest average speed. You can estimate by comparing the ratio of distance to time: the bike ride covers a much longer distance than the swim in a time only 3x longer, and covers 3x the run distance in a time only ~1.26x longer, so the bike speed is clearly the highest.

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For Question 13: