33. Se unen 3 pintores con las siguientes cualidades: El primero pinta 3 metros cuadrados en una hora. El segundo pinta 2 metros cuadrados y medio en 40 minutos. El tercero pinta la tercera parte de un metro cuadrado en un cuarto de hora. ¿Cuántas horas tardarán en pintar entre los tres una superficie de 485 metros cuadrados?

Para resolver el problema, primero debemos calcular la tasa de trabajo de cada pintor en metros cuadrados por hora. 1. **Primer pintor**: Pinta 3 metros cuadrados en 1 hora. - Tasa del primer pintor: \(3 \, \text{m}^2/\text{hora}\) 2. **Segundo pintor**: Pinta 2.5 metros cuadrados en 40 minutos. Primero convertimos 40 minutos a horas: - \(40 \, \text{minutos} = \frac{40}{60} \, \text{horas} = \frac{2}{3} \, \text{horas}\) - Tasa del segundo pintor: \[ \text{Tasa} = \frac{2.5 \, \text{m}^2}{\frac{2}{3} \, \text{horas}} = 2.5 \times \frac{3}{2} = 3.75 \, \text{m}^2/\text{hora} \] 3. **Tercer pintor**: Pinta \(\frac{1}{3}\) de metro cuadrado en un cuarto de hora. Primero convertimos un cuarto de hora a horas: - \( \frac{1}{4} \, \text{hora} = 0.25 \, \text{horas} \) - Tasa del tercer pintor: \[ \text{Tasa} = \frac{\frac{1}{3} \, \text{m}^2}{0.25 \, \text{horas}} = \frac{1}{3} \times \frac{1}{0.25} = \frac{1}{3} \times 4 = \frac{4}{3} \, \text{m}^2/\text{hora} \] Ahora sumamos las tasas de los tres pintores para obtener la tasa total de trabajo: \[ \text{Tasa total} = 3 \, \text{m}^2/\text{hora} + 3.75 \, \text{m}^2/\text{hora} + \frac{4}{3} \, \text{m}^2/\text{hora} \] Para sumar, primero convertimos \(3\) y \(3.75\) a fracciones con un denominador común de \(3\): - \(3 = \frac{9}{3}\) - \(3.75 = \frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \frac{15}{4} = \frac{45}{12} = \