document.write( "Question 1149845: a tank has 2 inlets P and Q and an outlet tap R .when empty the tank can be
\n" ); document.write( "filled by tap p alone in 4 and a half hours or by tap Q alone in 3hours.
\n" ); document.write( "when full the tank can be emptied in 2 hours by tap R
\n" ); document.write( "a) the tank is initially empty . find how long it would take to fill up the
\n" ); document.write( "tank i)if tap R is closed and taps P and Q are opened at the same time.
\n" ); document.write( "ii) if all the three taps are opened at the same time.
\n" ); document.write( "B) the tank is initially empty and the three taps are opened as follows:
\n" ); document.write( "P at 8:00 A.m Q at 8.45 A.m R at 9.00 A.m i)find the fraction of the
\n" ); document.write( "tank that would be filled by 9.00 a.m ii)find the time the tank would be
\n" ); document.write( "fully filled up.
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Algebra.Com's Answer #771183 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
a tank has 2 inlets P and Q and an outlet tap R .\r
\n" ); document.write( "\n" ); document.write( "when empty the tank can be filled by tap P alone in 4 and a half hours
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document.write( "So tap P's filling rate is 1 tank per 4 1/2 hours or\r\n" );
document.write( "1 tank per 9/2 hours or 1/(9/2) tank per hour or 2/9 tank per hour\r\n" );
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\n" ); document.write( "or by tap Q alone in 3 hours.
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document.write( "So tap P's filling rate is 1 tank per 3 hours or 1/3 tank per hour\r\n" );
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\n" ); document.write( "when full the tank can be emptied in 2 hours by tap R
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\r\n" );
document.write( "So tap R's emptying rate (negative filling rate) is -1 tank per 2 hours or\r\n" );
document.write( "-1/2 tank per hour\r\n" );
document.write( "

\n" ); document.write( "a) the tank is initially empty . find how long it would take to fill up the
\n" ); document.write( "tank i)if tap R is closed and taps P and Q are opened at the same time.
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\r\n" );
document.write( "Their combined rate is 2/9 + 1/3 = 2/9  + 3/9 = 5/9 tank/hour\r\n" );
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document.write( "In x hours they will fill 1 tank:\r\n" );
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document.write( "(5/9)x = 1\r\n" );
document.write( "     x = 9/5 = 1.8 hours = 1 hour and 48 minutes.\r\n" );
document.write( "

\n" ); document.write( "ii) if all the three taps are opened at the same time.
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document.write( "Their combined rate is 2/9 + 1/3 - 1/2 = 4/18  + 6/18 - 9/18 = 1/9 tank/hour\r\n" );
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document.write( "In x hours they will fill 1 tank:\r\n" );
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document.write( "(1/9)x = 1\r\n" );
document.write( "     x = 9 hours.\r\n" );
document.write( "

\n" ); document.write( "B) the tank is initially empty and the three taps are opened as follows:
\n" ); document.write( "P at 8:00 A.m Q at 8.45 A.m R at 9.00 A.m \r
\n" ); document.write( "\n" ); document.write( "i)find the fraction of the tank that would be filled by 9.00 a.m
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\r\n" );
document.write( "P has been open 1 hour at 9AM and since it fills 2/9 tank per hour it\r\n" );
document.write( "has filled 2/9 of the tank.\r\n" );
document.write( "Q has been open 15 minutes or 1/4 hour at 9AM and since it fills 1/3 of\r\n" );
document.write( "a tank per hour it has filled 1/4 of 1/3 or 1/12 tank.\r\n" );
document.write( "R hasn't opend yet, so the fraction of a tank that has been filled is\r\n" );
document.write( "2/9 + 1/12 = 8/36 + 3/36 = 11/36 of a tank.\r\n" );
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\n" ); document.write( "ii)find the time the tank would be fully filled up.
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\r\n" );
document.write( "It is 11/36 full at 9AM so it has 25/36 tank more to go, so in x hours after\r\n" );
document.write( "9AM it will fill the remaining 25/36 tank at the combined rate of 1/9 tank\r\n" );
document.write( "per hour, so\r\n" );
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document.write( "(1/9)x = 25/36\r\n" );
document.write( "     x = (25/36)(9/1) = 25/4 = 6 1/4 hours\r\n" );
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document.write( "6 hours 15 minutes after 9AM is 6:15PM.\r\n" );
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document.write( "Edwin

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