1. **Problem 1:** Three identical machines take 6 hours to empty a reservoir together. We need to find how long it takes for one machine to empty it alone. 2. The rate of work for three machines together is $$\frac{1}{6}$$ reservoir per hour. 3. Since the machines are identical, the rate of one machine is $$\frac{1}{3} \times \frac{1}{6} = \frac{1}{18}$$ reservoir per hour. 4. Therefore, the time taken by one machine alone to empty the reservoir is the reciprocal of its rate: $$\text{Time} = \frac{1}{\frac{1}{18}} = 18$$ hours. --- 1. **Problem 2:** Find the value of $$x$$ given the triangle with angles 40°, 100°, and $$x$$. 2. The sum of angles in a triangle is always 180°. 3. So, $$x = 180 - 40 - 100 = 40$$ degrees. --- 1. **Problem 3:** Solve the system of equations: $$x + 2y = 7$$ $$2x + y = 11$$ 2. Multiply the first equation by 2: $$2x + 4y = 14$$ 3. Subtract the second equation from this: $$(2x + 4y) - (2x + y) = 14 - 11$$ $$3y = 3$$ $$y = 1$$ 4. Substitute $$y=1$$ into the first equation: $$x + 2(1) = 7$$ $$x + 2 = 7$$ $$x = 5$$ 5. Find $$x + y$$: $$5 + 1 = 6$$