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

Question 2: A car consumes fuel at a rate inversely proportional to its speed. If at 60 km/h it consumes 8 liters per hour, what is its fuel consumption at 45 km/h? Show your working.

Answer: 10.67

Question 3: A bottle fills with water at a rate inversely proportional to the height of the water in the bottle. If it takes 10 minutes to fill a bottle to a height of 5 cm, how long will it take to fill it to 8 cm? Show your working.

Answer: 6.25

Question 4: A machine's speed is inversely proportional to the time taken for a task. If the machine completes a task in 12 hours at a certain setting, how long will it take at a setting where the speed doubles? Show your working.

Answer: 6

Question 5: A certain recipe requires 2 cups of sugar for 4 servings. If servings are increased and the sugar amount varies inversely with the number of servings, how much sugar is needed for 10 servings? Show your working.

Answer: 0.8

Question 6: A water tank empties at a rate inversely proportional to the height of the water. If it takes 15 minutes to drain when the water height is 10 cm, how long will it take when the height is 6 cm? Show your working.

Answer: 25

Question 7: A cyclist's speed varies inversely with the time taken to travel a fixed distance. If at a speed of 15 km/h the trip takes 4 hours, what is the speed if the trip takes 6 hours? Show your working.

Answer: 10

Question 8: A factory produces 240 units of a product in 8 hours. If production rate is inversely proportional to the number of workers, how many workers are needed to produce 360 units in 8 hours? Show your working.

Answer: 16

Question 9: A swimmer's time to complete a race is inversely proportional to her speed. If she completes a 100m race in 50 seconds at a certain speed, how long would it take her at a speed twice as fast? Show your working.

Answer: 25

Question 10: A gardener uses a certain amount of water to irrigate a field. The amount of water used is inversely proportional to the area irrigated. If 20 liters of water are needed for a 50 sq.m field, how much water is needed for a 80 sq.m field? Show your working.

Answer: 12.5

Question 11: A delivery truck's travel time decreases as the number of drivers increases, inversely proportional. If 3 drivers take 6 hours to complete a route, how long will it take 6 drivers? Show your working.

Answer: 3

Question 12: Error Identification: A student calculates that if 4 workers take 10 hours, then 8 workers will take 5 hours, treating the problem as directly proportional. Is this correct? If not, explain and correct the reasoning.

Answer: No, because the problem is inversely proportional; doubling workers halves the time, so 8 workers would take 5 hours, which is correct in this case. But if the student assumed direct proportion, they might think time stays the same, which is wrong.