A. The equation to find the distance of the flowerbed from the hive is: [tex]\frac{x}{20}+\frac{x}{12}+900= 1200[/tex] , where x is the distance.
B. The flowerbed is 2250 feet far from the hive.
Explanation
Suppose, the distance of the flowerbed from the hive is [tex]x[/tex] feet.
The bee flies 20 feet per second directly to a flowerbed from its hive and flies directly back to the hive at 12 feet per second.
As, [tex]Time=\frac{Distance}{Speed}[/tex]
So, the time taken by the bee to reach the flowerbed [tex]= \frac{x}{20}[/tex] seconds and the time taken to fly back to the hive [tex]=\frac{x}{12}[/tex] seconds.
The bee stays at the flowerbed for 15 minutes or (15×60)seconds or 900 seconds and it is away from the hive for a total of 20 minutes or (20×60)seconds or 1200 seconds.
So, the equation will be.......
[tex]\frac{x}{20}+\frac{x}{12}+900= 1200\\ \\ \frac{3x+5x}{60}= 300\\ \\ 8x= 60*300\\ \\ 8x=18000\\ \\ x=\frac{18000}{8}=2250[/tex]
Thus, the distance of the flowerbed from the hive is 2250 feet.
