Answer:
- 20 = x/360 +16 +x/240 . . . . equation for distance (x)
- 576 feet . . . . . distance to the flowerbed
Step-by-step explanation:
You want to write and solve an equation for the distance traveled by a bee to and from a flowerbed, given its flying rates and total trip time.
Speed
We are given times in minutes and speeds in feet per second, so a units conversion is necessary to put all of the times in the same units. It is probably convenient to convert the speeds.
 speed = (6 ft/s)×(60 s/min) = 360 ft/min . . . . from the hive
 speed = (4 ft/s)×(60 s/min) = 240 ft/min . . . . to the hive
Equation
The relationship between speed, distance, and time is ...
 time = distance/speed
The total time away from the hive is the sum ...
 time away = (time to flowerbed) + (time at flowerbed) +(time to hive)
Using the above relation for travel times, and the variable x to represent the distance between hive and flowerbed, we can write the equation ...
 20 = x/360 +16 +x/240 . . . . . . equation to find the distance
Distance
Subtracting 16 from the above equation and rearranging it, we get ...
 4 = x(1/360 +1/240)
 4 = x(2 +3)/720 . . . . . . . . . use a common denominator for the fractions
 4(144) = x . . . . . . . . . . . . multiply by 144
 x = 576 . . . . . . . the distance to the flowerbed in feet
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Additional comment
The 576 ft trip will take 576/6 = 96 seconds from the hive, and 576/4 = 144 seconds back to the hive. Then the time in the air is 96+144 = 240 seconds, or 4 minutes, consistent with the problem statement.
