Google tells me that one league is approximately 18228 feet.
The hound runs at a speed of 12 leagues an hour, or 1/5 league a minute.
In 5 minutes, the hound runs 1 league.
Now let us examine the progress of the fowl. Since its initial speed is 20 leagues/hr, in the first quarter-minute it runs 20/(4*60) = 20/240 of a league. In the second quarter-minute, its speed becomes 19 leagues/hr, which is equivalent to 19/(4*60) = 19/240 league per quarter-minute.
Thus in 5 minutes, the fowl runs:
20/240 + 19/240 + ... + 1/240 = (20 + ... + 1)/240 = (21*10)/240 = 7/8 of a league.
Recall that the hound, on the other hand, runs 1 league = 18228 feet in those 5 minutes, which is significantly greater than 7/8 of a league + 10 feet = 15949.5 + 10 feet = 15959.5 feet.
Hence we conclude that the hound catches the fowl.
Answer: Yes
No comments:
Post a Comment