Question 1: A car travels a certain distance at a speed of 60 km/h and takes 2 hours. If the speed is increased to 90 km/h, how long will it take to cover the same distance? Show your working.

Answer: 1 hour

Question 2: A pump fills a tank in 4 hours when working alone. When two identical pumps work together, how long will it take to fill the tank? Show your working.

Answer: 2 hours

Question 3: A worker takes 6 hours to complete a task. If another worker works at half the speed, how long will it take for both to complete the task if they work together? Show your working.

Answer: 4 hours

Question 4: A machine's efficiency is inversely proportional to the time it takes to produce a certain number of items. If the machine takes 5 hours to produce 100 items, how long will it take to produce the same number at double the efficiency? Show your working.

Answer: 2.5 hours

Question 5: A car's fuel consumption is inversely proportional to its speed. If at 60 km/h the car consumes 8 litres per 100 km, what is the fuel consumption at 80 km/h? Show your working.

Answer: 7.5 litres per 100 km

Question 6: A factory produces a certain number of units in 10 hours. If production rate increases such that time taken decreases proportionally, how long will it take to produce the same units if the rate doubles? Show your working.

Answer: 5 hours

Question 7: A cyclist maintains a speed inversely proportional to the time taken to complete a route. If it takes 3 hours at a certain speed, how long will it take if the cyclist doubles their speed? Show your working.

Answer: 1.5 hours

Question 8: A recipe requires 4 eggs to make 12 cookies. If the number of eggs is inversely proportional to the number of cookies, how many eggs are needed to make 24 cookies? Show your working.

Answer: 2 eggs

Question 9: A water tank empties at a rate inversely proportional to the time. If it takes 8 hours to empty the tank, how long will it take if the rate is doubled? Show your working.

Answer: 4 hours

Question 10: A gardener plants a certain number of trees in a day. If planting time is inversely proportional to the number of trees, how long will it take to plant 50 trees if it takes 2 days to plant 20 trees? Show your working.

Answer: 0.8 days

Question 11: A machine's output is inversely proportional to the time taken to produce a batch. If the machine produces 200 units in 4 hours, how many units will it produce in 2 hours? Show your working.

Answer: 400 units

Question 12: Error Analysis: A student calculates that doubling the speed of a vehicle halves the travel time. Identify the mistake if the actual travel time remains unchanged when the speed increases. Explain your reasoning.

Answer: Incorrect assumption; in inverse proportion, doubling speed halves time, but if time remains unchanged, this suggests a different relationship or an error.