Inverse Variation

It is a mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant

A type of variation in which the variable y varies inversely with the variable x

Inverse Variation

The quantity y varies inversely with x if there exists a nonzero constant k such that:y = or equivalently, xy = k

Also, y varies inversely as the nth power of x if there exists a nonzero real number k

Inverse Variation

A proportion can also be used in relation to indirect variation in solving problems where some quantities are known.X1y1 = k x2y2 = kx1y1 = x2y2

=

Inverse Variation

The number of hours (t), required to finish a certain job varies inversely as the number of persons (N) on the job. If 16 persons require 18 hours to finish the job, how long would it take 64 persons to finish the job?

Inverse Variation

Solution:Because t and N are in inverse proportion,tN = kWhen N = 16 and t = 18, 18(16) = k k = 288 t = 288

Inverse Variation

Solution:When N = 64, t(64) = 288 t = 4.5

The time to be taken by 64 workers to complete the job is 4.5 hours or 4 hours and 30 minutes

Inverse Variation