divs on top of eachother not minding their margins - html

Question

I have created several divs on top of each other .
Here is the problem that I'm having. The 2 divs in sessiondetails (sessionspeakers and sessionhosts) while they line up on top of themselves like I want them to, they don't listen to what I tell them to about padding. I want about 15px space between them, but they overlap eachother.
This is the html i am using:
<div class="sessiondetails">
<h3>Global Security Challenges and How We're Facing Them</h3>
Some of the biggest and most successful companies in the world depend on RSA's products and services for protection. Niloofar Howe, RSA's Chief Strategy Officer, is charged with making sure her company is responding to the needs of those customers by anticipating the next threat.<!-- Start of speaker list -->
<div class="sessionspeakers">
Speaker:<br><div class="speaker"><img src="http://www.structuresecurity.com/wp-content/uploads/2016/08/structuresecurityconf-niloo-howe.jpg" width="100px" height="100"><strong>Niloofar Howe</strong><br> Chief Strategy Officer, RSA</div>
</div> <!-- End of sessionspeakers list -->
<!-- Start of host list -->
<div class="sessionhosts">
Host:<br><strong>Mahendra Ramsinghani</strong>, Founder, Secure Octane
</div> <!-- End of sessionhosts list -->
</div>
This is my css:
.sessionentry {
width: 100%;
border-top: 1px solid grey;
border-top-color: grey;
border-bottom: 1px solid grey;
border-bottom-color: grey;
clear: both;
vertical-align: top;
overflow: hidden;
padding: 20px 0;
}
.sessiontime {
width: 15%;
float: left;
display: inline-block;
padding-left: 15px;
}
.sessiondetails {
width: 75%;
float: left;
display: inline-block;
}
.sessionmoderator, .sessionspeakers, .sessionhosts, .sessionemcee {
margin-top: 15px;
clear: both;
float: left;
}
.speaker {
overflow: visible;
display: block;
clear: both;
}
.speaker img {
float: left;
margin-right: 15px;
}
So can some kind soul please tell me what I did wrong?
Here are two images of the problem:
Sessionspeakers section doesn't go down far enough:
and then sessionhosts (div on bottom looks too high and covers part of photo)