document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206959>Question 1206959</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Water is leaking fron a tank at a constant rate . At 230pm the tank is 3/5 full .At 325pm the tank was 2/7 full. At what time will the tank be empty.<BR>\n" );
document.write( "Thanks </SPAN>\n" );
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document.write( "Answer:  <font color=red size=4>4:15 PM</font>\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "x = number of minutes after 2:30 PM<BR>\n" );
document.write( "y = fraction representing how full the tank is.<BR>\n" );
document.write( "y = 0 means the tank is completely empty.<BR>\n" );
document.write( "y = 1 means the tank is completely full.\r<BR>\n" );
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document.write( "The water is leaking at a constant rate. Which will mean we can use a linear equation. \r<BR>\n" );
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document.write( "We have the two points on this line which are (0,3/5) and (55, 2/7)<BR>\n" );
document.write( "The 55 refers to 55 minutes after 2:30 PM to arrive at 3:25 PM.\r<BR>\n" );
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document.write( "Note: The jump from 2:30 to 3:30 is 1 hour, aka 60 minutes, so we subtract off 5 minutes to go from 2:30 to arrive at 3:25.\r<BR>\n" );
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document.write( "I'll skip a few steps but the equation of the line through those points mentioned is y = (-1/175)x + 3/5\r<BR>\n" );
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document.write( "We want to know when the tank will be empty, so we want to determine x when y = 0.\r<BR>\n" );
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document.write( "y = (-1/175)x + 3/5<BR>\n" );
document.write( "0 = (-1/175)x + 3/5<BR>\n" );
document.write( "(1/175)x = 3/5<BR>\n" );
document.write( "x = 175*(3/5)<BR>\n" );
document.write( "x = 105<BR>\n" );
document.write( "It takes 105 minutes to go from 3/5 full to completely empty.\r<BR>\n" );
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document.write( "105 min = 60 min + 45 min<BR>\n" );
document.write( "105 min = 1 hr + 45 min\r<BR>\n" );
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document.write( "Now add this duration to 2:30 to see where we end up.<BR>\n" );
document.write( "From 2:30 to 3:30 is 1 hour.<BR>\n" );
document.write( "From 3:30 to 4:00 is 30 minutes.<BR>\n" );
document.write( "From 4:00 to <font color=red>4:15</font> is another 15 minutes (30+15 = 45 minutes total)\r<BR>\n" );
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document.write( "Or...<BR>\n" );
document.write( "The jump from 2:30 PM to 4:30 PM is 2 hours<BR>\n" );
document.write( "Rewind the clock 15 minutes to go from 4:30 PM to <font color=red>4:15 PM</font><BR>\n" );
document.write( "Rewinding those 15 minutes means the 2 hour duration is adjusted to 1 hour+45 minutes. \r<BR>\n" );
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document.write( "Therefore, the time gap from 2:30 PM to <font color=red>4:15 PM</font> is 1 hour+45 minutes aka 105 minutes.\r<BR>\n" );
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document.write( "--------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Tutor @mananth made a mistake.<BR>\n" );
document.write( "The tank doesn't start off 100% full, so we don't need to drain 100% of the contents. <BR>\n" );
document.write( "Instead we need to drain 3/5 = 0.6 = 60% of the contents.\r<BR>\n" );
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document.write( "If you solved (11/35)/55 = 1/x then you'll get x = 175<BR>\n" );
document.write( "While this is a correct solution to this equation, the equation itself is set up wrong. <BR>\n" );
document.write( "The \"1\" on the right hand side should be 3/5 to represent the fractional amount we need to drain.<BR>\n" );
document.write( "The \"1\" on the right hand side represents 100% full. \r<BR>\n" );
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document.write( "If you solved (11/35)/55 = (3/5)/x, then you'll get x = 105 which then leads to <font color=red>4:15 PM</font> as mentioned above.<BR>\n" );
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