Direct and Inverse Proportion：练习题

It is given that \( z \) is directly proportional to \( x^2 \). When \( x = 2 \), \( z = 12 \). Find the value of \( z \) when \( x = 5 \).

It is given that \( a \) is inversely proportional to \( b \). If \( a = 8 \) when \( b = 5 \), find the value of \( a \) when \( b = 20 \).

It is given that \( y \) is inversely proportional to \( x \). When \( x = 4 \), \( y = 9 \). Find the value of \( y \) when \( x = 6 \).

A car travels 150 km on 10 litres of petrol. How many kilometres can it travel on 18 litres of petrol?

It is given that \( y \) is directly proportional to \( x \). When \( x = 12 \), \( y = 8 \).
(a) Find the equation connecting \( x \) and \( y \).
(b) Find the value of \( x \) when \( y = 10 \).

The time (\( T \)) taken to complete a task is inversely proportional to the number of workers (\( W \)). If 6 workers can finish the task in 10 hours:
(a) Find the time taken if only 4 workers are available.
(b) If the task must be finished in 4 hours, how many workers are needed?