Ratio Variations Questions

The electrical current \( I \) in a conductor varies inversely as the resistance \( R \) (in ohms). If the current is 12 A when the resistance is 240 Ω, what is the current when the resistance is 540 Ω?

Hooke’s Law states that the distance \( s \) that a spring is stretched varies directly with the mass \( m \) of the object. If the spring stretches 18 cm with a 3 kg mass, how far will it stretch with a 5 kg mass?

The volume \( V \) of an ideal gas at constant temperature varies inversely with the pressure \( P \). If the volume is 200 cm³ at 32 kg/cm², what is the volume at 40 kg/cm²?

The number of aluminum cans \( c \) used each year varies directly as the number of people \( p \). If 250 people use 60,000 cans in one year, how many cans would 1,000,000 people use?

The time \( t \) to complete a masonry job varies inversely with the number of bricklayers \( b \). If 7 bricklayers can finish the job in 5 hours, how long would it take 10 bricklayers?

The wavelength \( \lambda \) of a radio signal varies inversely with its frequency \( f \). A wave with a frequency of 1200 kilohertz has a wavelength of 250 meters. What is the wavelength when the frequency is 60 kilohertz?

The amount of water \( w \) in a human body is directly proportional to the body mass \( m \). If a 96 kg person contains 64 kg of water, how much water is in a 60 kg person?

The time \( t \) to drive a fixed distance varies inversely with speed \( v \). If it takes 5 hours at 80 km/h, what speed is needed to make the same trip in 4.2 hours?

The volume \( V \) of a cone varies jointly as its height \( h \) and the square of its radius \( r \). If a cone with a height of 8 cm and radius of 2 cm has a volume of 33.5 cm³, what is the volume of a cone with a height of 6 cm and radius of 4 cm?