How can I use the Lerp the right way ? The duration is set to 10 but the transform is moving too fast and not in 10 seconds as I wanted.

Question

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class MoveToTarget : MonoBehaviour
{
    public enum TransitionState
    {
        None,
        MovingTowards,
        Transferring
    }

    public Transform destinationTransform;
    public bool isChild = false;
    public AnimationCurve curve = AnimationCurve.EaseInOut(0.0f, 0.0f, 1.0f, 1.0f);
    public float duration = 10.0f;
    public bool go = false;

    private float t;
    private Transform originTransform;
    private float timer;
    private TransitionState state = TransitionState.MovingTowards;
    private Vector3 originPosition;
    private SphereCollider col;
    private bool enableCollider = true;

    void Start()
    {
        t = 0.0f;

        curve.postWrapMode = WrapMode.Once;
        originPosition = transform.position;
        col = GetComponent<SphereCollider>();
    }

    void Update()
    {
        if (go)
        {
            if (col != null && enableCollider)
            {
                Destroy(col);
                Destroy(transform.GetComponent<Rigidbody>());
                transform.GetComponent<InteractableItem>().enabledInteraction = false;

                enableCollider = false;
            }

            switch (state)
            {
                case TransitionState.MovingTowards:
                    var v = destinationTransform.position - transform.position;
                    if (v.magnitude < 0.001f)
                    {
                        state = TransitionState.Transferring;
                        originTransform = destinationTransform;
                        timer = 0;
                        return;
                    }

                    t += Time.deltaTime;
                    float s = t / duration;

                    transform.position = Vector3.Lerp(transform.position,
                        destinationTransform.position, curve.Evaluate(s));

                    break;

                case TransitionState.Transferring:
                    timer += Time.deltaTime;
                    this.transform.position = Vector3.Lerp(originTransform.position, destinationTransform.position, timer);

                    if (timer >= 1.0f)
                    {
                        this.transform.parent = destinationTransform;
                        transform.localPosition = new Vector3(0, 0, 0);
                        isChild = true;

                        go = false;

                        state = TransitionState.None;
                        this.enabled = false;
                        return;
                    }
                    break;

                default:
                    this.enabled = false;
                    return;
            }
        }
    }
}

When the transform is moving to the target(destinationTransform) even if the duration is set to 10 the transform is moving very fast and get the target after 2-3 seconds not 10.
I want the transform to move using the duration by seconds.

Something is wrong with the way I'm using the lerp in this part :

 t += Time.deltaTime;
                        float s = t / duration;

                        transform.position = Vector3.Lerp(transform.position,
                            destinationTransform.position, curve.Evaluate(s));

I guess I'm using the Lerp in the right way.

And in the second place I'm also not sure if I'm using the right way with the Lerp :

this.transform.position = Vector3.Lerp(originTransform.position, destinationTransform.position, timer);