Six pipes can fill the tank in 80 minutes, therefore one pipe fills the tank in 80 minutes / 6 pipes = 13.33 minutes. Four pipes will fill the tank in 13.33 minutes * 4 pipes = 53.33 minutes.
The food is enough for 50 students for 40 days, therefore it's enough for one student for 40 days / 50 students = 0.8 days. If 30 more students join the group, the food is enough for 50 students + 30 students = 80 students, for 0.8 days / student. So, the food will last for 80 students * 0.8 days/student = 64 days.
Five trucks can transport 120 tons in 2 days, therefore one truck can transport 120 tons / 5 trucks = 24 tons in 2 days. Three trucks can transport 24 tons/truck * 3 trucks = 72 tons in 2 days. In 4 days, they will transport 72 tons * 2 days = 144 tons.
Four machines categorize 8000 packages in 8 hours, therefore one machine categorizes 8000 packages / 4 machines = 2000 packages in 8 hours. To categorize 4500 packages in 6 hours, the number of machines needed is 4500 packages / (2000 packages/machine * 8 hours/6 hours) = 4500 packages / (2000 packages/machine * 4/3) = 4500 / (2000 * 4/3) = 4500 / 2667 ≈ 1.68 machines, which is approximately 2 machines.
Five machines can produce 5000 units of soap in 2 days, therefore one machine can produce 5000 units / 5 machines = 1000 units in 2 days. Ten machines can produce 1000 units/machine * 10 machines = 10 000 units in 2 days. In five days, they will produce 10 000 units * 5 days = 50 000 units.