{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 23: Clocks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 23.1, Page number 23.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "required time is 16.36 minutes past 3\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "H=3;     #initial position of hour hand\n",
    "A=0;    #required angle(degrees)\n",
    "\n",
    "#Calculation\n",
    "T=(2/11)*((H*30)+A);    #required time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"required time is\",round(T,2),\"minutes past\",H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 23.2, Page number 23.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "one timing is 38.18 minutes past 4\n",
      "another timing is 5.45 minutes past 4\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "H=4;     #initial position of hour hand\n",
    "A=90;    #required angle(degrees)\n",
    "\n",
    "#Calculation\n",
    "T1=(2/11)*((H*30)+A);    #required time(minutes)\n",
    "T2=(2/11)*((H*30)-A);    #required time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"one timing is\",round(T1,2),\"minutes past\",H\n",
    "print \"another timing is\",round(T2,2),\"minutes past\",H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 23.3, Page number 23.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "one timing is 54.545 minutes past 7\n",
      "another timing is 21.818 minutes past 7\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "H=7;     #initial position of hour hand\n",
    "A=90;    #required angle(degrees)\n",
    "\n",
    "#Calculation\n",
    "T1=(2/11)*((H*30)+A);    #required time(minutes)\n",
    "T2=(2/11)*((H*30)-A);    #required time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"one timing is\",round(T1,3),\"minutes past\",H\n",
    "print \"another timing is\",round(T2,3),\"minutes past\",H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 23.4, Page number 23.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "required time is 5.45 minutes past 7\n",
      "answer given in the book is wrong\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "H=7;     #initial position of hour hand\n",
    "A=180;    #required angle(degrees)\n",
    "\n",
    "#Calculation\n",
    "T=(2/11)*((H*30)-A);    #required time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"required time is\",round(T,2),\"minutes past\",H\n",
    "print \"answer given in the book is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 23.5, Page number 23.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "one timing is 34.909 minutes past 5\n",
      "another timing is 19.636 minutes past 5\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "H=5;     #initial position of hour hand\n",
    "A=42;    #required angle(degrees)\n",
    "\n",
    "#Calculation\n",
    "T1=(2/11)*((H*30)+A);    #required time(minutes)\n",
    "T2=(2/11)*((H*30)-A);    #required time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"one timing is\",round(T1,3),\"minutes past\",H\n",
    "print \"another timing is\",round(T2,3),\"minutes past\",H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 23.6, Page number 23.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true time is 55.08 minutes past 5 p.m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "Ti=6-1;      #time interval(hours)\n",
    "h=1/60;    #hour gained(hour)\n",
    "\n",
    "\n",
    "#Calculation\n",
    "Tti=Ti/(1+h);     #true time interval(hours)\n",
    "Tt=1+Tti;       #true time(hours)\n",
    "H=int(Tt);      #hour hand(p.m)\n",
    "m=(Tt-H)*60;    #true time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"true time is\",round(m,2),\"minutes past\",H,\"p.m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 23.7, Page number 23.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "required time is 27.27 minutes past 2 and at 3 o' clock\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "H=2;     #initial position of hour hand\n",
    "A=90;    #required angle(degrees)\n",
    "\n",
    "#Calculation\n",
    "T1=(2/11)*((H*30)+A);    #required time(minutes)\n",
    "T2=(2/11)*((H*30)-A);    #required time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"required time is\",round(T1,2),\"minutes past\",H,\"and at\",H+1,\"o' clock\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 23.8, Page number 23.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total time gained is 5.035 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "T=12;    #time(hours)\n",
    "x=65;    #time(minutes)\n",
    "y=65+(5/11);     #time interval(minutes)\n",
    "\n",
    "#Calculation\n",
    "Ttg=(T*60)*(y-x)/x;      #total time gained(minutes)\n",
    "\n",
    "#Result\n",
    "print \"total time gained is\",round(Ttg,3),\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 23.9, Page number 23.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "required time is 16.36 minutes and 49.09 minutes past 12\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "H=0;     #initial position of hour hand\n",
    "A=90;    #required angle(degrees)\n",
    "\n",
    "#Calculation\n",
    "T1=(2/11)*((H*30)+A);    #required time(minutes)\n",
    "T2=(2/11)*(360+(H*30)-A);    #required time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"required time is\",round(T1,2),\"minutes and\",round(T2,2),\"minutes past 12\""
   ]
  }
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