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Deshawn and Tyriq can weed their garden in 30 minutes together. Alone, it takes Tyriq 75 minutes to weed the garden. How long does it take Deshawn to weed the garden alone? ◻ minutes

Deshawn and Tyriq can weed their garden in 3030 minutes together. Alone, it takes Tyriq 7575 minutes to weed the garden.\newlineHow long does it take Deshawn to weed the garden alone?\newline□\square minutes

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Q. Deshawn and Tyriq can weed their garden in 3030 minutes together. Alone, it takes Tyriq 7575 minutes to weed the garden.\newlineHow long does it take Deshawn to weed the garden alone?\newline□\square minutes
  1. Define Deshawn's time: question_prompt: How long does it take Deshawn to weed the garden alone?
  2. Calculate Deshawn's rate: Let's call the time it takes Deshawn to weed the garden alone DD minutes.
  3. Calculate combined rate: The rate at which Deshawn works is 1D\frac{1}{D} of the garden per minute. Tyriq's rate is 175\frac{1}{75} of the garden per minute. Together, their rate is 130\frac{1}{30} of the garden per minute.
  4. Set up equation: Add their rates together to get the combined rate: 1D+175=130\frac{1}{D} + \frac{1}{75} = \frac{1}{30}.
  5. Clear fractions: Multiply all terms by 30D30D to clear the fractions: 30(1D)+30(175)=30(130)30\left(\frac{1}{D}\right) + 30\left(\frac{1}{75}\right) = 30\left(\frac{1}{30}\right).
  6. Simplify equation: Simplify the equation: 30+30D75=D30 + \frac{30D}{75} = D.

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