Question 1: If 5 workers can complete a task in 8 hours, how long would it take 10 workers to complete the same task? Show your working.

Answer: 4 hours

Question 2: A car consumes fuel inversely proportional to its speed. If at 60 km/h, the car consumes 8 liters per hour, what is its fuel consumption at 40 km/h? Show your working.

Answer: 12 liters per hour

Question 3: Construct a graph to represent the relationship between speed (x-axis) and fuel consumption (y-axis), given that fuel consumption varies inversely with speed. Plot the points for speeds of 40 km/h and 60 km/h with their respective consumptions.

Answer: Graph showing the inverse relation, with points (40, 12) and (60, 8)

Question 4: A recipe requires 3 cups of sugar for 4 servings. If the number of servings increases to 12, how many cups of sugar are needed? Show your working.

Answer: 9 cups

Question 5: A machine's efficiency is inversely proportional to the time taken to complete a task. If the machine takes 5 hours to complete a job with a certain setting, how long will it take if the efficiency doubles? Explain your reasoning.

Answer: It will take 2.5 hours because efficiency doubles, so time halves.

Question 6: A cyclist's speed and travel time are inversely proportional. If traveling at 30 km/h takes 6 hours, what is the maximum speed if the cyclist wants to complete the journey in 3 hours? Show your working.

Answer: 60 km/h

Question 7: A factory produces 150 units of a product in 5 hours with a certain machine. If the production rate is inversely proportional to the machine's downtime, estimate how many units can be produced in 8 hours assuming the machine's downtime doubles. Show your working.

Answer: 300 units

Question 8: A photocopier's copying speed (pages per minute) is inversely proportional to the number of copies being made simultaneously. If making 20 copies takes 4 minutes, how many minutes will it take to make 10 copies? Show your working.

Answer: 2 minutes

Question 9: A water tank fills at a rate inversely proportional to the amount of water already in the tank. If it takes 10 minutes to fill to 20 liters, how long will it take to fill to 50 liters? Explain your reasoning.

Answer: It will take 25 minutes because the rate decreases as volume increases.

Question 10: A scientist is conducting an experiment where the rate of a reaction is inversely proportional to the temperature in Celsius. If at 30°C, the reaction takes 15 minutes, estimate the time at 60°C. Show your working.

Answer: 7.5 minutes

Question 11: Error Analysis: A student states that if the number of workers doubles, the time to complete a task halves, and this applies only to situations where the workers are equally skilled. Identify a common mistake in this reasoning and explain how to correct it.

Answer: The mistake is assuming inverse proportion always applies without considering skill or other factors. The correction is that inverse proportion applies only when the variable relationship is directly proportional and other factors remain constant.