a bee flies at 20 feet per second directly to a flowerbed from its hive. the bee stays at the flowerbed for 12 minutes, and then flies directly back to the hive at 12 feet per second. it is away from the hive for a total of 17 minutes. what equation can you use to find the distance of the flowerbed from the hive?

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Convert time to seconds: Convert the total time the bee is away from the hive into seconds. The bee is away for a total of 17 minutes. Since there are 60 seconds in a minute, we multiply 17 minutes by 60 seconds per minute to get the total time in seconds. 17 minutes * 60 seconds/minute = 1020 seconds.Calculate time at flowerbed: Convert the time the bee stays at the flowerbed into seconds. The bee stays at the flowerbed for 12 minutes. Again, we multiply by 60 seconds per minute to convert this time into seconds. 12 minutes * 60 seconds/minute = 720 seconds.Calculate time spent flying: Calculate the time spent flying. The total time the bee is away includes the time spent at the flowerbed and the time spent flying to and from the flowerbed. To find the time spent flying, we subtract the time spent at the flowerbed from the total time away. Total time flying = Total time away - Time at flowerbed Total time flying = 1020 seconds - 720 seconds = 300 seconds.Find distance to flowerbed: Let the distance to the flowerbed be represented by the variable d (in feet). We need to find this distance, d, which the bee travels at two different speeds: 20 feet per second on the way to the flowerbed and 12 feet per second on the way back.Equation for distance to flowerbed: Write the equation for the distance traveled to the flowerbed. The bee flies to the flowerbed at 20 feet per second. Let t1 be the time in seconds it takes to get to the flowerbed. The distance d can be expressed as: d = 20 * t1Equation for distance from flowerbed: Write the equation for the distance traveled from the flowerbed back to the hive. The bee flies back to the hive at 12 feet per second. Let t2 be the time in seconds it takes to get back to the hive. The distance d is the same, so it can also be expressed as: d = 12 * t2Combine time equations: Since the bee flies directly to the flowerbed and then directly back, the times t1 and t2 must add up to the total flying time. Therefore, we have the equation: t1 + t2 = 300 secondsExpress time in terms of distance: Express t1 and t2 in terms of d using the equations from Steps 5 and 6. From Step 5: t1 = d / 20 From Step 6: t2 = d / 12Substitute time expressions: Substitute the expressions for t1 and t2 into the equation from Step 7. (d / 20) + (d / 12) = 300Find common denominator: Find a common denominator to combine the terms on the left side of the equation. The common denominator for 20 and 12 is 60. We rewrite the equation as: (3d / 60) + (5d / 60) = 300Combine terms: Combine the terms on the left side of the equation. (3d + 5d) / 60 = 300 8d / 60 = 300Solve for distance: Multiply both sides of the equation by 60 to solve for d. 8d = 300 * 60 8d = 18000Divide both sides of the equation by 8 to find the value of d. d = 18000 / 8 d = 2250

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