Steps:
Energy: 

SOLVING:
Steps To Go: 0	Energy Left: 0	Seconds: 0


PAGE SOURCE:
<html>
<body>

<?php
$steps = 0;
$energy = 0;
if( isset( $_POST['steps'] ) && is_numeric( $_POST['steps'] ) )
    $steps = $_POST['steps'];
if( isset( $_POST['energy'] ) && is_numeric( $_POST['energy'] ) )
    $energy = $_POST['energy'];
?>

<form action="" method="post">
Steps: <input type="text" name="steps" value="<?php echo $steps; ?>" /><br  />
Energy: <input type="text" name="energy" value="<?php echo $energy; ?>" /><br />
<input type="submit" /><br />
</form>

<pre>
<?php


echo "SOLVING:\n";
solve( $steps, $energy );


echo "\nPAGE SOURCE:";
highlight_file( "index.php" );


function solve( $steps, $energy )
{
    //define the speeds
    $speed = array(
            array( "steps" => 3, "energy" => 5, "seconds" => 2, "name" => "fast" ),
            array( "steps" => 2, "energy" => 3, "seconds" => 1.5, "name" => "medium" ),
            array( "steps" => 1, "energy" => 1, "seconds" => 1, "name" => "slow" )
        );

    //input validation
    if( $steps > $energy )
    {
        echo "** Not enough energy **\n";
        return;
    }

    //init
    $seconds = 0;

    //output progress
    echo "Steps To Go: {$steps}\tEnergy Left: {$energy}\tSeconds: {$seconds}\n\n";

    //try for all 3 speeds, fastest first
    for( $x=0; $x<3; $x++ )
    {

        //slowest speed is base case, or if energy and steps is the same
        if( $x == 2 || $energy == $steps )
        {
            //if taking steps in base case, do it
            if( $steps > 0 )
            {
                $moves = $steps;
                //consume steps to go and energy
                $steps -= $moves;
                $energy -= $moves;
                $seconds += $moves;

                //output progress
                echo "==> Take {$moves} slow step(s)\n\n";
                echo "Steps To Go: {$steps}\tEnergy Left: {$energy}\tSeconds: {$seconds}\n\n";
            }
            return;
        }
        else
        {
            //determine max moves by steps
            $moves_max_step = floor( $steps / $speed[$x]['steps'] );

            //determine max moves by energy consumption
            $moves_max_eng = floor( $energy / $speed[$x]['energy'] );

            //calculate max (ideal) moves that can be taken while maintaining steps >= energy
            //solving algebraicly for moves in:  steps - moves * steps at this speed = energy - moves * energy at this speed
            $moves_ideal = floor( ( $energy - $steps ) / ( $speed[$x]['energy'] - $speed[$x]['steps'] ) );

            //determine moves based on ideal and maximums
            $moves = min( $moves_ideal, $moves_max_step, $moves_max_eng );
            
            //if we are taking any moves at this speed, do it
            if( $moves > 0 )
            {
                //consume steps to go and energy
                $steps -= $moves * $speed[$x]['steps'];
                $energy -= $moves * $speed[$x]['energy'];
                $seconds += $moves * $speed[$x]['seconds'];

                //output progress
                echo "==> Take {$moves} {$speed[$x]['name']} step(s)\n\n";
                echo "Steps To Go: {$steps}\tEnergy Left: {$energy}\tSeconds: {$seconds}\n\n";
            }
        }
    }
}
?>
</pre>
</body>
</html>