{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 19: Time and Distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.1, Page number 19.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "distance covered is 700.0 m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "s=3.5;      #speed(km/h)\n",
    "t=12/60;    #time(hr)\n",
    "\n",
    "#Calculation\n",
    "d=s*t*1000;     #distance covered(m)\n",
    "\n",
    "#Result\n",
    "print \"distance covered is\",d,\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.2, Page number 19.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time taken is 2 hour 45 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d=124;     #distance(km)\n",
    "s=45;      #speed(km/h)\n",
    "\n",
    "#Calculation\n",
    "t=d/s;      #time(hr)\n",
    "tm=(t-int(t))*60;     #time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"time taken is\",int(t),\"hour\",int(tm),\"minutes\"    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.3, Page number 19.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time taken is 5.0 hours\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d=360*1000;     #distance(m)\n",
    "v=20;      #velocity(m/s)\n",
    "\n",
    "#Calculation\n",
    "t=d/v;     #time taken(min)\n",
    "\n",
    "#Result\n",
    "print \"time taken is\",t/(60*60),\"hours\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.4, Page number 19.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total time taken is 50.0 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "n=4;    #number of rests\n",
    "tr=5;    #time for each rest(min)\n",
    "d=5;    #distance(km)\n",
    "s=10;   #speed(km/hr)\n",
    "\n",
    "#Calculation\n",
    "rt=n*tr;   #rest time(min)\n",
    "t=(d*60/s)+rt;   #total time taken(min)\n",
    "\n",
    "#Result\n",
    "print \"total time taken is\",t,\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.5, Page number 19.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "usual time is 15.0 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "abyb=5/7;    #factor\n",
    "deltat=6;    #change in time(min)\n",
    "\n",
    "#Calculation\n",
    "bbya=1/abyb;      \n",
    "t=deltat/(bbya-1);     #usual time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"usual time is\",t,\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.6, Page number 19.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "usual time is 28.0 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "abyb=7/6;    #factor\n",
    "deltat=4;    #change in time(min)\n",
    "\n",
    "#Calculation\n",
    "bbya=1/abyb;      \n",
    "t=deltat/(1-bbya);     #usual time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"usual time is\",t,\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.7, Page number 19.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "distance is 5.0 km\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "t=10+5;     #difference in time(min)\n",
    "v1=4;    #speed(km/h)\n",
    "v2=5;    #speed(km/h)\n",
    "\n",
    "#Calculation\n",
    "d=v1*v2*t/60;     #distance(km)\n",
    "\n",
    "#Result\n",
    "print \"distance is\",d,\"km\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.8, Page number 19.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slower speed of train is 25.0 km/h\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "t1=8;     #time(hr)\n",
    "t2=6+(40/60);     #time(hr)\n",
    "d=5;     #distance(km)\n",
    "\n",
    "#Calculation\n",
    "v=d/((t1/t2)-1);     #slower speed of train(km/h)\n",
    "\n",
    "#Result\n",
    "print \"slower speed of train is\",v,\"km/h\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.9, Page number 19.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train stops at 15.0 minutes/hour\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "s1=80;    #speed(km/h)\n",
    "s2=60;    #speed(km/h)\n",
    "\n",
    "#Calculation\n",
    "st=(s1-s2)/s1;     #stoppage time(hr)\n",
    "\n",
    "#Result\n",
    "print \"train stops at\",st*60,\"minutes/hour\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.10, Page number 19.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "distance is 60.0 km\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "x=4;     #speed(km/h)\n",
    "a=30/60;    #time(hr)\n",
    "y=2;    #speed(km/h)\n",
    "b=20/60;    #time(hr)\n",
    "\n",
    "#Calculation\n",
    "d=(x+y)*(a+b)*a*b*x*y/((b*x)-(a*y))**2;        #distance(km)\n",
    "\n",
    "#Result\n",
    "print \"distance is\",d,\"km\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.11, Page number 19.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "distance ran by theif is 800.0 m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d=400;     #distance(m)\n",
    "s1=10;     #speed(km/h)\n",
    "s2=15;     #speed(km/h)\n",
    "\n",
    "#Calculation\n",
    "x=d*s1/(s2-s1);     #distance ran by theif(m)\n",
    "\n",
    "#Result\n",
    "print \"distance ran by theif is\",x,\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.12, Page number 19.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average speed is 70.0 km/h\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d1=450;       #distance(km)\n",
    "d2=740;       #distance(km)\n",
    "t1=7;         #time(hrs)\n",
    "t2=10;        #time(hrs)\n",
    "\n",
    "#Calculation\n",
    "Va=(d1+d2)/(t1+t2);     #average speed(km/h)\n",
    "\n",
    "#Result\n",
    "print \"average speed is\",Va,\"km/h\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.13, Page number 19.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average speed is 48.0 km/h\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "V1=60;      #speed(km/h)\n",
    "V2=40;      #speed(km/h)\n",
    "\n",
    "#Calculation\n",
    "Va=2*V1*V2/(V1+V2);     #average speed(km/h)\n",
    "\n",
    "#Result\n",
    "print \"average speed is\",Va,\"km/h\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.14, Page number 19.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average speed is 63 km/h\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "V1=40;      #speed(km/h)\n",
    "V2=60;      #speed(km/h)\n",
    "V3=70;      #speed(km/h)\n",
    "t1=30/60;         #time(hrs)\n",
    "t2=45/60;        #time(hrs)\n",
    "t3=2;         #time(hrs)\n",
    "\n",
    "#Calculation\n",
    "Va=((V1*t1)+(V2*t2)+(V3*t3))/(t1+t2+t3);     #average speed(km/h)\n",
    "\n",
    "#Result\n",
    "print \"average speed is\",int(Va),\"km/h\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.15, Page number 19.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time taken to travel is 2.0 hours\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "V1=60;      #speed(km/h)\n",
    "V2=30;      #speed(km/h)\n",
    "d=240;      #distance(km)\n",
    "t=6;        #time(hrs)\n",
    "\n",
    "#Calculation\n",
    "Va=d/t;     #average speed(km/h)\n",
    "t60=Va-V2;\n",
    "t30=V1-Va;\n",
    "T=t60*t/(t60+t30);      #time taken to travel(hours)\n",
    "\n",
    "#Result\n",
    "print \"time taken to travel is\",T,\"hours\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.16, Page number 19.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "distance travelled by car is 140 km\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",
    "t=2;     #time(hrs)\n",
    "v1=100;    #speed(km/h)\n",
    "v2=50;     #speed(km/h)\n",
    "d=170;     #distance(km)\n",
    "\n",
    "#Calculation\n",
    "x=(t*d)-(t*v1);      #distance travelled by car(km)\n",
    "\n",
    "#Result\n",
    "print \"distance travelled by car is\",x,\"km\"\n",
    "print \"answer given in the book is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.17, Page number 19.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total distance is 3.0 km\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "T=42;     #total time(min)\n",
    "v1=4;    #speed(km/h)\n",
    "v2=5;     #speed(km/h)\n",
    "\n",
    "#Calculation\n",
    "d=T/(v1+(2*v2));     #total distance(km)\n",
    "\n",
    "#Result\n",
    "print \"total distance is\",d,\"km\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.18, Page number 19.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original speed is 60.0 km/h\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d=840;     #distance(km)\n",
    "t=2;     #time(hrs)\n",
    "s=10;    #speed(km/h)\n",
    "\n",
    "#Calculation\n",
    "x=d*s/(s*t);    \n",
    "y=x/(t*(t+1));\n",
    "V=d*s/(t*y);      #original speed(km/h)\n",
    "\n",
    "#Result\n",
    "print \"original speed is\",V,\"km/h\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.19, Page number 19.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total time taken is 6 1/4 hrs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import Fraction\n",
    "\n",
    "#Variable declaration\n",
    "tx=4+(30/60);      #time(hrs)\n",
    "ty=1+(45/60);      #time(hrs)\n",
    "\n",
    "#Calculation\n",
    "T=tx+ty;        #total time taken(hrs)\n",
    "x=T-int(T);\n",
    "\n",
    "#Result\n",
    "print \"total time taken is\",int(T),Fraction(x),\"hrs\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.20, Page number 19.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time taken by A is 100 min\n",
      "time taken by B is 80 min\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "rA=4;\n",
    "rB=5;     #rates of A and B\n",
    "t=20;     #time(min)\n",
    "\n",
    "#Calculation\n",
    "tB=rA*t;   #time taken by B(min)\n",
    "tA=t*rB;   #time taken by A(min)\n",
    "\n",
    "#Result\n",
    "print \"time taken by A is\",tA,\"min\"\n",
    "print \"time taken by B is\",tB,\"min\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 19.21, Page number 19.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total time taken is 4.33 hrs\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "t=6+(30/60);      #time(hrs)\n",
    "tl=2+(10/60);      #time lost(hrs)\n",
    "\n",
    "#Calculation\n",
    "T=t-tl;        #total time taken(hrs)\n",
    "\n",
    "#Result\n",
    "print \"total time taken is\",round(T,2),\"hrs\""
   ]
  }
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