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# Average Speed

## Question

An athlete wants to compete in a race. The race requires the athlete to swim to set buoy and back and then trek up a hillside. Practicing the athlete noticed that it takes her 3 hours to make it to the buoy and back. Going back for her was much faster (2 miles per hour less). Going up hill, she was able to run in some parts and walk in others. She ran 3 miles in 20 minutes and walked an average of .08 miles per minute. If she swam for 8 miles and walked for 10 minutes, what was her average speed throughout the exercise?

## 2 answers to this question

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Average Speed = Total distance / Total time

• Swim: 8 miles over 3 hours
• Run: 3 miles over 20 minutes = 1/3 hours
• Walk: 10 minutes * 0.08 miles per minute = 0.8 miles over 1/6 hours

Average speed = Total Distance / Total Time = 11.8 miles / 3.5 hours = 3.371428... mph = 3 13/35 mph

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I got the same solution as above, however there are many types of averages. You could take a distance-weighted average, considering that most of the distance was spent in the water, given that a greater contribution to the average, making the average speed 4.42 mph. Or you could take a time-weighted average, which would be close to the answer of total distance/total time.

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