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
