Hover on div(1) to show div(2), if mouseout continue to show div(2) for x seconds

Question

When I hover on the image, div(2) appears.
But I want div(2) to remain about x seconds even on mouse out.

I only want to use PURE CSS. How can I do it?

jsFiddle

#basarilar {
  float: right;
  margin: 7px 357px;
  width: 140px;
  height: 24px;
  position: relative;
  z-index: 9999;
}
.yildiz {
  height: 24px;
  width: 24px;
  background: url("http://www.kelimelerbenim.com/wp-content/themes/kelimelerbenim/images/yildiz.png") 0 0 no-repeat;
  margin-left: 10px;
  float: right;
  transition: .50s all;
  transition-delay: 5s;
}
.yildiz:hover {
  background: url("http://www.kelimelerbenim.com/wp-content/themes/kelimelerbenim/images/yildiz-2.png") 0 0 no-repeat;
}
.aciklama {
  display: none;
  position: absolute;
  width: 200px;
  height: 70px;
  z-index: 9999;
  top: 48px;
  right: 0px;
  padding: 15px 15px;
  font-weight: bold;
  text-align: center;
}
#bumerang1 {
  color: #ffffff;
  background: #76ab01;
}
#bumerang:hover + #bumerang1 {
  display: block;
}
#bumerang1:hover {
  display: block;
}

<div id="basarilar">
  <div id="bumerang" class="yildiz"></div>
  <div id="bumerang1" class="aciklama">This is my DIV</div>
</div>

Answer 1

Christopher Pearson was right about using transition-delays, but you'll need to change a couple of other things as well.

#basarilar {
    float:right;
    margin:7px 357px;
    width: 140px;
    height: 24px;
    position: relative;
    z-index: 9999;
}
.yildiz {
    height:64px;
    width:64px;
    background:url("https://i.sstatic.net/vNQ2g.png?s=64&g=1") no-repeat;
    margin-left:10px;
    float:right;
    transition: .50s all;
    transition-delay: 5s;
}
.yildiz:hover {
    background:url("https://i.sstatic.net/vNQ2g.png?s=64&g=1") 0 0 no-repeat;
}
.aciklama {
    visibility: hidden; /* use visibility rather than display */
    position:absolute;
    width: 200px;
    height: 70px;
    z-index: 9999;
    top:48px;
    right:0px;
    padding: 15px 15px;
    font-weight: bold;
    text-align: center;
    transition-delay: 3s; /* Set transition-delay to 3s, so the mouse out is delayed */ 
}
#bumerang1 {
    color:#ffffff;
    background: #76ab01;
}
#bumerang:hover + #bumerang1 {
    visibility: visible; /* use visibility rather than display */
    transition-delay: 0s; /* Set transition-delay to 0s, so the mouse over is still immediate */ 
}
#bumerang1:hover {
    display:block;
}

<div id="basarilar">
    <div id="bumerang" class="yildiz"></div>
    <div id="bumerang1" class="aciklama">This is my DIV</div>
</div>