A) The equation that we need to solve is:
(12ft/s)*(- d/(15ft/s) + 300s) = d
B) The distance to the hive is d = 2000ft.
<h3 /><h3>What equation can you use to find the distance of the flower bed from the hive?</h3>
We know that the bee's speed is 15 ft/s from the hive to the flower bed.
Then stays 12 minutes at the flower bed.
Then returns to the hive with a speed of 12ft/s.
The total time of the journey is 17 minutes, discounting the 12 minutes that the bee was in the flower bed, the travel only took 5 minutes.
Now, if the distance between the hive and the flower bed is d, t₁ as the time that the bee needs to go from the hive to the flower bed, and t₂ as the time in which the bee goes from the flower bed to the hive, we can write the system of equations:
t₂ + t₁ = 5min
(15ft/s)*t₁ = d
(12ft/s)*t₂ = d
With that system of equations, we can find the value of d, which is what we want to get.
Isolating t₂ in the first equation we get:
t₂ = - t₁ + 5min
Now we can replace that in the third equation:
(15ft/s)*t₁ = d
(12ft/s)*(- t₁ + 5min) = d
In the first equation we can isolate t₁:
t₁ = d/(15ft/s)
And replace that in the remaining equation:
(12ft/s)*(- d/(15ft/s) + 5min) = d
5 min = 5*60s = 300s
(12ft/s)*(- d/(15ft/s) + 300s) = d
This is the equation we need to solve to find the value of d.
-(12/15)*d + 3600ft = d
3600ft = d + (12/15)*d = (1 + 12/15)*d = (27/15)*d
(15/27)*3600ft = d = 2000 ft
We conclude that the distance to the hive is 2000ft.
If you want to learn more about systems of equations:
brainly.com/question/13729904
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