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5. Three people are planting tomatoes in a community garden. Marta takes
50 minutes to plant the garden alone, Benito takes x minutes and Tyler takes
x + 15 minutes. If the three of them take 20 minutes to finish the garden,
how long would it have taken Tyler alone?

Respuesta :

The time it will take for Tyler to finish planting tomatoes alone is; 75 minutes

Understanding Work Proportion

We are told that three people are planting tomatoes in a community garden. The time each alone takes to plant are;

  • Marta = 50 minutes
  • Benito = x minutes
  • Tyler = x + 15 minutes

Thus, their individual rates are;

  • Marta = 1/50
  • Benito = 1/x
  • Tyler = 1/(x + 15)

Since together, they take 20 minutes, then it means that;

1/50 + 1/x + 1/(x + 15) = 1/20

Multiply through by x(x + 15) to get;

(x² + 15x)/50 + (x + 15) + x = (x² + 15x)/20

Multiply through by 100 to get;

2(x² + 15x) + 100(x + 15) + 100x = 5(x² + 15x)

100x + 1500 + 100x = 5(x² + 15x) - 2(x² + 15x)

200x + 1600 = 3x² + 45x

3x² - 155x - 1600 = 0

Solving this using quadratic formula calculator online gives;

x ≈ 60

Thus, the time it will take tyler alone to finish is;

60 + 15 = 75 minutes

Read more about Work Proportion at; https://brainly.com/question/1781657

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