A runner runs 15.5 miles one day, one-half that distance the next day, 15.5 miles the next day, one-half that distance the next day, and so on. Over a period of several days running with this pattern, the runner runs a total of 372 miles.
How many days did it take the runner to run 372 miles? enter in the box
[ ] days
To find the number of days it took the runner to run a total of 372 miles, we need to find the sum of the distances the runner ran each day until reaching 372 miles.
Let's set up the pattern:
Day 1: 15.5 miles
Day 2: 15.5/2 = 7.75 miles (one-half of the previous day's distance)
Day 3: 15.5 miles
Day 4: 15.5/2 = 7.75 miles
...
It is clear that the pattern repeats every 4 days.
So, if we divide 372 miles by the sum of one complete pattern (15.5 + 7.75 + 15.5 + 7.75), we can determine how many times the pattern repeats, and therefore the number of days it took the runner to reach 372 miles.
372 miles / (15.5 + 7.75 + 15.5 + 7.75) miles = 372 miles / 46.5 miles = 8 complete patterns
Since each pattern takes 4 days, the runner took a total of 8 * 4 = 32 days to run 372 miles.
Answer: [32] days