how to make an object track the other object's exact movements

hey guys, so this script helps me to to tell the follower object to copy exact movements of the leader object ,i found this script in unity forums and it works pretty good acutely. but my question is how can i add some kind speed variable to it .how can i tell the follower object to move at lower speed? using System.Collections; using System.Collections.Generic; using UnityEngine; using UnityEngine.UI;

 public class delayTracker : MonoBehaviour
 {
 
    
 
     float progress;
     const int MAX_FPS = 60;
 
     public Transform leader;
     public float lagSeconds = 0.5f;
 
     Vector3[] _positionBuffer;
     float[] _timeBuffer;
     int _oldestIndex;
     int _newestIndex;
 
     // Use this for initialization
     void Start()
     {
         int bufferLength = Mathf.CeilToInt(lagSeconds * MAX_FPS);
         _positionBuffer = new Vector3[bufferLength];
         _timeBuffer = new float[bufferLength];
 
         _positionBuffer[0] = _positionBuffer[1] = leader.position;
         _timeBuffer[0] = _timeBuffer[1] = Time.time;
 
         _oldestIndex = 0;
         _newestIndex = 1;
     }
 
 
     void LateUpdate()
     {
                 // Insert newest position into our cache.
         // If the cache is full, overwrite the latest sample.
         int newIndex = (_newestIndex + 1) % _positionBuffer.Length;
         if (newIndex != _oldestIndex)
             _newestIndex = newIndex;
 
         _positionBuffer[_newestIndex] = leader.position;
         _timeBuffer[_newestIndex] = Time.time;
 
         // Skip ahead in the buffer to the segment containing our target time.
         float targetTime = Time.time - lagSeconds;
         int nextIndex;
         while (_timeBuffer[nextIndex = (_oldestIndex + 1) % _timeBuffer.Length] < targetTime)
             _oldestIndex = nextIndex;
 
         // Interpolate between the two samples on either side of our target time.
         float span = _timeBuffer[nextIndex] - _timeBuffer[_oldestIndex];
         float progress = 0f;
         if (span > 0f)
         {
             progress = (targetTime - _timeBuffer[_oldestIndex]) / span;
         }
 
         transform.position = Vector3.Lerp(_positionBuffer[_oldestIndex], _positionBuffer[nextIndex], progress );
     }
 
     void OnDrawGizmos()
     {
         if (_positionBuffer == null || _positionBuffer.Length == 0)
             return;
 
         Gizmos.color = Color.grey;
 
         Vector3 oldPosition = _positionBuffer[_oldestIndex];
         int next;
         for (int i = _oldestIndex; i != _newestIndex; i = next)
         {
             next = (i + 1) % _positionBuffer.Length;
             Vector3 newPosition = _positionBuffer[next];
             Gizmos.DrawLine(oldPosition, newPosition);
             oldPosition = newPosition;
         }
     }
 }