A bee flies at 15 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 14 minutes, and then flies directly back to the hive at 9 feet per second. It is away from the hive for a total of 16 minutes. A. What equation can you use to find the distance of the flowerbed from the hive? B. How far is the flowerbed from the hive?

9514 1404 393

  A) d/900 +14 +d/540 = 16

  B) 675 feet

Step-by-step explanation:

A) The times are all given in minutes, so it is convenient to use units of feet and minutes in this problem. There are 60 seconds in a minute, so the bee's speeds can be rewritten as ...

  15 ft/s = (15 ft/s)(60 s/min) = 900 ft/min

  9 ft/s = (9 ft/s)(60 s/min) = 540 ft/min

We know that time is the ratio of distance to speed, so for distance d, we have a total time of ...

  d/900 +14 +d/540 = 16

B) To solve the equation, we can subtract 14, then combine the fractions. Here, we choose to combine the fractions in a straightforward way, not being too concerned about "least common denominator." We use the formula ...

  a/b + c/d = (ad +bc)/(bd)

  (540d +900d)/(900·540) = 2 . . . . subtract 14, combine fractions

  d = 2(900)(540)/(1440) = 675

The flowerbed is 675 feet from the hive.