A red cart and a green cart, both traveling at speed \(v\) on a low-friction track, approach each other head-on. The red cart is moving to the right; the green cart, whose inertia is three times that of the red cart, is moving to the left. A black cart that has a spring on its left end and putty on its right end sits on the track between the two moving carts. The moving carts hit the black cart at the same instant. After the collision, the red cart moves left at speed \(v\), and the green and black carts move together at speed \(v / 5\). What is the inertia of the black cart, expressed as a multiple of the inertia of the red cart?