Check this out:
<!DOCTYPE html>
<html>
<head>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.2/jquery.min.js"></script>
<script>
$(document).ready(function () {
$("input[name='Round_trip']").on('click', function () {
if ($("input[name='Round_trip']:checked").val() === 'hide')
$("#returnFlightInfo").fadeOut();
else
$("#returnFlightInfo").fadeIn();
echo($("input[name='Round_trip']:checked").val());
});
})
</script>
</head>
<body>
<input type="radio" name="Round_trip" value="show" checked>Show
<input type="radio" name="Round_trip" value="hide">Hide
<br>
<p id="returnFlightInfo">Return Flight Info...</p>
</body>
</html>