Question

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?

Answer 1

9514 1404 393

Answer:

A) d/900 +14 +d/540 = 16

B) 675 feet

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.