Two solid metal spheres, \(X\) and \(Y\), have equal masses and are initially at the same temperature. Sphere \(X\) is made of a metal with specific heat capacity \(c_X = 2c_Y\), where \(c_Y\) is the specific heat capacity of Sphere \(Y\). Both spheres are heated by identical heating elements that deliver thermal energy at the same constant rate \(P\) until both spheres undergo the same temperature increase \(\Delta T\). Which of the following correctly compares the time \(\Delta t_X\) required to heat Sphere \(X\) to the time \(\Delta t_Y\) required to heat Sphere \(Y\), and provides a correct justification?