I have a border around my .tab-content and the same border around active .tabs. I've tried adding a transparent border on the bottom to no avail.

Is there a way to, where two borders overlap, have one override the other? Or is there a better way to accomplish this?
Here's a jsfiddle to show my basic set up.
.tab-content {
height:200px;
width:400px;
background-color: #aaa;
border:1px solid #000;
}
.tabs-container {
height:auto;
width:400px;
background-color:#aaabbb;
}
.tabs {
width:360px;
margin-left:20px;
}
.tab {
display:inline-block;
padding:5px 20px;
}
.tab.active {
border-left:1px solid #000;
border-right:1px solid #000;
border-top:1px solid #000;
border-bottom:transparent;
background-color: #aaa;
}
<div class="tabs-container">
<div class="tabs">
<div class="tab active">This Tab</div>
<div class="tab">That Tab</div>
</div>
</div>
<div class="tab-content">
</div>