Question

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 directly back to the hive at 12 ft./s it is away from the high for a total of 17 minutes. A. What equation can you use to find the distance of the flower bed from the hive. B. How far is the flower bed from the hive

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.