A bee flies at 15 ft./s directly into a flower bed from a time the beast stays at the flower bed for 12 minutes and then flies dir

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1. 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.

   What equation can you use to find the distance of the flower bed from the hive?

   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:

   https://brainly.com/question/13729904

   #SPJ1

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