Keeping Rigidbody on Moving Platform?

Hi, I've been recently trying to keep the controlled player, of which is controlled by a rigidbody, to stay on a moving platform in my 2D Platformer project. However, the player doesn't move with the moving platform. Here's my code:

 using UnityEngine;
 using System.Collections;
 
 public class PlayerPlatformMove : MonoBehaviour {
 
     // Use this for initialization
     void Start () {
     
     }
     
     // Update is called once per frame
     void Update () {
     
     }
     void OnTriggerStay2D(Collider2D other)
     {
         if (other.gameObject.tag == "MovingPlatform")
         {
             transform.parent = other.transform;
 
         }
     }
     void OnTriggerExit2D(Collider2D other)
     {
         if (other.gameObject.tag == "MovingPlatform")
         {
             transform.parent = null;
         }
     }
 }

Any help would be appreciated.

UPDATE: It seems as if the parenting method does work, but for some reason the player moves at a slower speed as opposed to the platform, despite it now being a child of the platform. Here's my code for the player:

 using UnityEngine;
 using System.Collections;
 
 public class Player : MonoBehaviour {
     public float jump;
     public float movespeed;
     public float moveactual;
     public bool grounded=true;
     public bool finish=false;
     public int score = 0;
     public int orglev = 0;
     public int jumpcount = 0;
     public Transform prefab;
     void Start () {
 
     
     }
     
 
     void Update () {
         if (grounded) {
             if (Input.GetKeyDown (KeyCode.Space)||Input.GetKeyDown(KeyCode.UpArrow)||Input.touchCount==1) {
                 
 
 
                 GetComponent<Rigidbody2D> ().velocity = new Vector2 (GetComponent<Rigidbody2D> ().velocity.x, jump);
                 
 
             }
         }
         if (transform.position.y < -20) {
             Application.LoadLevel ("Level1");
         }
 
         moveactual = 0;
         if (Input.GetKey (KeyCode.D)||Input.GetKey(KeyCode.RightArrow)) {
             moveactual=movespeed;
         }
         if (Input.GetKey (KeyCode.A)||Input.GetKey(KeyCode.LeftArrow)) {
             moveactual=-movespeed;
         }
         GetComponent<Rigidbody2D> ().velocity = new Vector2 (moveactual, GetComponent<Rigidbody2D> ().velocity.y);
        
 
 
 
     }
     void OnTriggerEnter2D(Collider2D other){
         if (other.tag == "Hills" || other.tag =="MovingPlatform") {
             grounded = true;
         }
         if (other.tag == "Finish") {
             finish = true;
             orglev = orglev + 1;
 
         }
         if (other.tag == "Coin") {
             Destroy (other.gameObject);
             score++;
             Debug.Log(score);
         }
     }
     void OnTriggerExit2D(){
         grounded = false;
     }
     void OnGUI(){
         GUI.Label (new Rect (100, 200, 20, 20), score.ToString());
         if (finish) {
             if(GUI.Button (new Rect (Screen.width / 2 - 100, Screen.height / 2 + 10, 150, 20), "Next Level")){
                 
                     Application.LoadLevel(orglev);
                 orglev = orglev + 1;
                 
                 
             }
         }
 
 
 
     }
     
 
 }
 

Why is that happening? Any help would again be appreciated.