let

h = the age of Harvey

j = the age of Jane

Harvey is 3 times as old as Jane

h = 3j

The sum of their ages is 48 years

h + j = 48

by solving the system of equations

h = 3j

h + j = 48

we find

h = 36 years

j = 12 years

click here to see the step by step solution of the system of equations

Harvey is 36 years of age.

Jane is 12 years of age.