Question

A bee flies 6 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 12 minutes, and then flies directly back to the hive at 4 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? Let d be the distance of the flowerbed from the hive.

Answer 1

Let's define some variables:

d = distance from the flowerbed to the hive

s1 = speed going from the hive to the flowerbed = 6 ft/s

s2 = speed going from the flowerbed back to the hive = 4 ft/s

The bee is away from the hive for a total of

16 minutes = 16 mn * 60 s/mn = 960 seconds

The bee stays at the flowerbed for 12 minutes, so total travel time in both directions is

16 minutes - 12 minutes = 4 minutes = 4 mn * 60 s/mn = 240 seconds

t1 = time going from hive to flowerbed

t2 = time going from flowerbed to hive

t = total travel time = t1 + t2 = 240 sec

t2 = 240 - t1

speed = distance/time

distance = speed * time

Going:

d = s1 * t1

d = 6t1

Returning:

d = s2 * t2

d = 4t2

The distances are equal, so

6t1 = 4t2

Now we substitute t2 with 240 - t1 to have an equation in a single variable.

$6t_1 = 4(240 - t_1)$

$6t_1 = 960 - 4t_1$

$10t_1 = 960$

$t_1 = 96$

The time to go from the hive to the flowerbed is 96 seconds.

$d = s_1t_1$

$d = 6 \dfrac{ft}{s} \times 96~seconds = 576~ft$

The equation for going to the hive is

$d = s_1t_1$

$d = 6 \times 96$

$d = 576 ~ft$

The distance is 576 ft.

Answer 2

Remark

You have to do a little subtracting and a little interpreting to get the answer. First you must assume that the bee travels in a straight line. This is math so we can assume this is true, although thousands would disagree.

Second you must assume that because it is loaded with nectar that it travels at a slower rate (not an unreasonable assumption).

Third you have to assume that the distance there is the same distance as coming back. Again this is math. We can make this assumption.

Find the travelling time.

The bee spends 12 minutes hunting down the nectar in the flowerbed. Since it was away from the hive for a total of 16 minutes, the travelling time is

16min - 12min = 4 min

Convert the Minutes to seconds.

1 minute = 60 seconds

4 minutes = 4*60 = 240 seconds.

Find the time each way.

The total time is 240 seconds, but it is not divided evenly.

Let the time there = t

Let the time back = 240 - t

The distances are the same.

r = 6 m/s

r1 = 4 m/s

t1 = t

t2 = 240 - t

dthere = dback

d = rate * time

6 m/s *t = 4 m/s (240 - t)      Remove the brackets on the right.

6 * t = 4*240 - 4t                  Combine the like terms on the right.

6t = 960 - 4t                         Add 4t to both sides

6t + 4t = 960 - 4t + 4t          Combine

10t = 960                              Divide both sides by 10

10t/10 = 960/10                    Do the division

t = 96                                    Time going to the flower bed

Find the distance

d = ?

r = 6 m/s

t = 96 second

d = r*t

d = 6 * 96 = 576 feet Answer