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A bee flies at 9 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 15 ​minutes, and then flies directly back to the hive at 6 feet per second. It is away from the hive for a total of 19 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?

Respuesta :

theleangreenbean
Answer:
A) What equation can you use to find the distance of the flowerbed from the hive?
You can use the formula distance=time*speed

B) How far is the flowerbed from the hive?
14.4 feet

Explanation:
1) We can set up a system of equations since there are many values that we don’t know, like how long the bee took to get to the flowerbed and back:

Variables:
a=the time it took for the bee to go to the flowerbed
b=the time it took for the bee to come back to the hive

Equation 1:
Distance when the bee went to the flowerbed=distance when the bee came back to the hive

Equation 2:
a+b+15=19
(In total it took the bee 19 minutes, but it stayed at the flowerbed for 15 minutes. a and b are how long it took to get there and back)

2) Then, we input the values in the first equation:

9*60*a=6*60*

The formula we use on both sides of the equation is d=t*s since both sides refer to the distance.

The reason we multiplied 60 to the speeds is because the speeds were in seconds, whereas the time values in the question are all minutes (ex. 9ft/s, 15 minutes on the flowerbed, etc.)

3) Then, we evaluate the first equation:

9*60*a=6*60*
Divide both sides by 60
9a=6b
Divide both sides by 3 (we do this to simplify the numbers)
3a=2b

4) Now, we move around the second equation to bring into the first equation:

a+b+15=19
Combined like terms
a+b=19-15
a+b=4
a=4-b

5) Bring the second equation into the first:

3a=2b
3(4-b)=2b
Multiply the parentheses
12-3b=2b
Combine like terms
12=2b+3b
12=5b
Divide both sides by 5 (to cancel it out)
12/5=5b/5
12/5=b
b=2.4 minutes

6) From here, we can solve for the distance.

Distance=time*speed
Because we found b, the time it took for the bee to come back to the hive, we need to use the same speed
Distance=2.4*6
Distance=14.4

I hope this helps! If it did, a brainliest would be much appreciated :)
boffeemadrid

The equation to find the distance and the distance between the flower bed and hive is required.

The required equation is [tex]\text{Distance}=\text{Speed}\times\text{Time}[/tex] and the distance between the flowerbed and hive is 864 feet.

Speed of the bee when it travels from hive to flowerbed = 9 ft/s

Speed of the bee when it travels from flowerbed to hive = 6 ft/s

Let [tex]t_1[/tex] be the time taken for the bee to travel from hive to flowerbed

[tex]t_2[/tex] be the time taken for the bee to travel from flowerbed to hive.

The bee remained in the flower bed for 15 minutes.

The bee was away from the hive for 19 minutes.

So, time taken to travel from the hive to the flowerbed and return is

[tex]19-15=4\ \text{minutes}=240\ \text{seconds}[/tex]

So,

[tex]t_1+t_2=240\\\Rightarrow t_1=240-t_2[/tex]

Distance between the hive and flowerbed, and flowerbed and hive is same

[tex]\text{Distance}=\text{Speed}\times\text{Time}[/tex]

[tex]9t_1=6t_2[/tex]

The required equation is [tex]\text{Distance}=\text{Speed}\times\text{Time}[/tex]

[tex]9(240-t_2)=6t_2\\\Rightarrow 2160-9t_2=6t_2\\\Rightarrow t_2=\dfrac{2160}{15}\\\Rightarrow t_2=144\ \text{s}[/tex]

So, time taken to travel from the flowerbed to the hive is 144 s.

Distance would be

[tex]6\times 144=864\ \text{ft}[/tex]

The distance between the flowerbed and hive is 864 feet.

Learn more:

https://brainly.com/question/23774048

https://brainly.com/question/17824245

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