document.write( "Question 503580: A 90,000 gallon water tank can be filled in two hours by opening valve A alone and in two and a half hours by opening valve B alone. It can be emptied in three hours by opening valve C alone. How long will it take to fill the tank under each of the following conditions? If an answer is not whole hours, include hours, minutes and seconds in your answer.\r
\n" ); document.write( "\n" ); document.write( " a. Valve B is kept closed. Valves A and C are opened
\n" ); document.write( " b. Valve C is kept closed. Valves A and B are opened
\n" ); document.write( " c. Valve A is kept closed. Valves B and C are opened
\n" ); document.write( " d. valve C is kept closed. Valve A is opened. Twenty minutes later valve B is also opened
\n" ); document.write( " e. Valves A and C are opened. Twenty minutes later valve B is also opened
\n" ); document.write( " f. Valve A is opened. Twenty minutes later valves B and C are also opened
\n" ); document.write( " g. Valve C is kept closed. Valve A is opened. Valve B is also opened twenty minutes later and is then closed after another ten minutes
\n" ); document.write( " h. Valve C is kept closed. Valve A is opened. Twenty minutes later valve B is also opened. Ten minutes after that, Valve A is closed
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Algebra.Com's Answer #339366 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
A 90,000 gallon water tank can be filled in two hours by opening valve A alone and in two and a half hours by opening valve B alone. It can be emptied in three hours by opening valve C alone. How long will it take to fill the tank under each of the following conditions? If an answer is not whole hours, include hours, minutes and seconds in your answer.
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document.write( "To avoid so many fractions, let's use minutes:\r\n" );
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document.write( "A tank can be filled in 120 minutes by opening valve A alone and in 150 \r\n" );
document.write( "minutes by opening valve B alone. It can be emptied in 180 minutes by \r\n" );
document.write( "opening valve C alone. \r\n" );
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document.write( "Make this chart. Fill in 1's for the number of tanks filled, and -1 for C,\r\n" );
document.write( "since to empty a tank is mathematically the sames as \"filling -1 tanks\".\r\n" );
document.write( "Fill in the times required as stated in the problem: \r\n" );
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document.write( "                               Number of      Time in       Rate in\r\n" );
document.write( "                               Tanks filled     minutes       tanks/hour\r\n" );
document.write( "       A only                        1            120         \r\n" );
document.write( "       B only                        1            150         \r\n" );
document.write( "       C only                       -1            180        \r\n" );
document.write( "     \r\n" );
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document.write( "Now fill in the rates in tanks/hour by dividing the number of tanks\r\n" );
document.write( "filled by the the number of hours\r\n" );
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document.write( "                               Number of      Time in       Rate in\r\n" );
document.write( "                               Tanks filled     minutes       tanks/hour\r\n" );
document.write( "       A only                        1            120         1/120\r\n" );
document.write( "       B only                        1            150         1/150\r\n" );
document.write( "       C only                       -1            180        -1/180\r\n" );
document.write( "\r\n" );
document.write( "Now we'll bring in condition \"a\":  Fill in 1 for the number of tanks filled\r\n" );
document.write( "x for the number of minutes required and fill in the rate by dividing\r\n" );
document.write( "number of tanks filled by minutes.\r\n" );
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document.write( "                               Number of      Time in       Rate in\r\n" );
document.write( "                               Tanks filled     minutes       tanks/hour\r\n" );
document.write( "       A only                        1            120         1/120\r\n" );
document.write( "       B only                        1            150         1/150\r\n" );
document.write( "       C only                       -1            180        -1/180\r\n" );
document.write( "  a. A&C only                        1             x            1/x                                              \r\n" );
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document.write( "We use\r\n" );
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document.write( "  , answer 360 minutes = 6 hours\r\n" );
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document.write( "Now we'll bring in condition \"b\":  Fill in 1 for the number of tanks filled\r\n" );
document.write( "x for the number of minutes required and fill in the rate by dividing\r\n" );
document.write( "number of tanks filled by minutes.\r\n" );
document.write( "\r\n" );
document.write( "                               Number of      Time in       Rate in\r\n" );
document.write( "                               Tanks filled     minutes       tanks/hour\r\n" );
document.write( "       A only                        1            120         1/120\r\n" );
document.write( "       B only                        1            150         1/150\r\n" );
document.write( "       C only                       -1            180        -1/180\r\n" );
document.write( "  b. A&B only                        1             x            1/x                                              \r\n" );
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document.write( "We use\r\n" );
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document.write( "  , answer 66 2/3 minutes or\r\n" );
document.write( "1 hour, 6 minutes, 40 seconds  \r\n" );
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document.write( "---------------------\r\n" );
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document.write( "Now we'll bring in condition \"c\":  Fill in 1 for the number of tanks filled\r\n" );
document.write( "x for the number of minutes required and fill in the rate by dividing\r\n" );
document.write( "number of tanks filled by minutes.\r\n" );
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document.write( "                               Number of      Time in       Rate in\r\n" );
document.write( "                               Tanks filled     minutes       tanks/hour\r\n" );
document.write( "       A only                        1            120         1/120\r\n" );
document.write( "       B only                        1            150         1/150\r\n" );
document.write( "       C only                       -1            180        -1/180\r\n" );
document.write( "  c. B&C only                        1             x            1/x                                              \r\n" );
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document.write( "We use\r\n" );
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document.write( "  , answer 900 minutes = 15 hours\r\n" );
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document.write( "Now we'll bring in condition \"d\", which is in two parts.\r\n" );
document.write( "For the first 20 minutes fill in A's rate, 1/120 and 20 for the time in minutes:\r\n" );
document.write( "Then fill in the \"tanks filled\" by multiplying rate by the time, getting \r\n" );
document.write( "20/120 or 1/6 of a tank filled.  Then put x for the number of minutes after the\r\n" );
document.write( "first 20 minutes, and the sum of A's and B's rates 1/120 + 1/150 = 3/200.\r\n" );
document.write( "Then to find the number of tanks filled we multiple the rate by the time,\r\n" );
document.write( "and get (3/200)x  \r\n" );
document.write( "\r\n" );
document.write( "                               Number of      Time in       Rate in\r\n" );
document.write( "                               Tanks filled     minutes       tanks/hour\r\n" );
document.write( "       A only                        1            120         1/120\r\n" );
document.write( "       B only                        1            150         1/150\r\n" );
document.write( "       C only                       -1            180        -1/1\r\n" );
document.write( "d1. A only for 20 min              1/6            20          1/120 \r\n" );
document.write( "d2. A&B only after 20 minutes    (3/200)x          x          3/200\r\n" );
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document.write( "We use\r\n" );
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document.write( "  , answer 500/9 minutes \r\n" );
document.write( "= 55 minutes 33 1/3 seconds.\r\n" );
document.write( "Adding on the first 20 minutes, 75 minutes, 33 1/3 seconds or\r\n" );
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document.write( "1 hour, 15 minutes, 33 1/3 seconds. \r\n" );
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document.write( "---------------------------\r\n" );
document.write( "\r\n" );
document.write( "Now we'll bring in condition \"e\", which is also in two parts.\r\n" );
document.write( "For the first 20 minutes fill in A&C's rate, 1/120-1/180 = 1/72, and\r\n" );
document.write( "20 minutes for the time \r\n" );
document.write( "Then fill in the \"tanks filled\" by multiplying rate by the time, getting \r\n" );
document.write( "20/120 or 1/6 of a tank filled.  Then put x for the number of minutes after the\r\n" );
document.write( "first 20 minutes, and the sum of A's,B's, and C's rates \r\n" );
document.write( "1/120 + 1/150 - 1/180 = 17/1800.\r\n" );
document.write( "Then to find the number of tanks filled we multiple the rate by the time,\r\n" );
document.write( "and get (3/200)x  \r\n" );
document.write( "\r\n" );
document.write( "                               Number of      Time in       Rate in\r\n" );
document.write( "                               Tanks filled     minutes       tanks/hour\r\n" );
document.write( "       A only                        1            120         1/120\r\n" );
document.write( "       B only                        1            150         1/150\r\n" );
document.write( "       C only                       -1            180        -1/180\r\n" );
document.write( "e1. A&C only for 20 minutes        5/18            20         1/72 \r\n" );
document.write( "e2. A&B&C after 20 minutes    (17/1800)x            x        17/1800  \r\n" );
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document.write( "We use\r\n" );
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document.write( "  , answer 1300/17 minutes \r\n" );
document.write( "= 76 minutes 28 4/17 seconds.\r\n" );
document.write( "Adding on the first 20 minutes, 96 minutes, 28 4/17 seconds or\r\n" );
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document.write( "1 hour, 36 minutes, 28 4/17 seconds. \r\n" );
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document.write( "---------------------------\r\n" );
document.write( "---------------------------\r\n" );
document.write( "\r\n" );
document.write( "Now we'll bring in condition \"f\", which is also in two parts.\r\n" );
document.write( "For the first 20 minutes fill in As rate, 1/120, and\r\n" );
document.write( "20 minutes for the time \r\n" );
document.write( "Then fill in the \"tanks filled\" by multiplying rate by the time, getting \r\n" );
document.write( "20/120 or 1/6 of a tank filled.  Then put x for the number of minutes after the\r\n" );
document.write( "first 20 minutes, and the sum of A's,B's, and C's rates \r\n" );
document.write( "1/120 + 1/150 - 1/180 = 17/1800.\r\n" );
document.write( "Then to find the number of tanks filled we multiple the rate by the time,\r\n" );
document.write( "and get (3/200)x  \r\n" );
document.write( "\r\n" );
document.write( "                               Number of      Time in       Rate in\r\n" );
document.write( "                               Tanks filled     minutes       tanks/hour\r\n" );
document.write( "       A only                        1            120         1/120\r\n" );
document.write( "       B only                        1            150         1/150\r\n" );
document.write( "       C only                       -1            180        -1/180\r\n" );
document.write( "f1. A for 20 minutes                1/6            20          1/120 \r\n" );
document.write( "f2. A&B&C after 20 minutes    (17/1800)x            x        17/1800\r\n" );
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document.write( " We use\r\n" );
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document.write( "  , answer 1500/17 minutes \r\n" );
document.write( "= 88 minutes 14 2/17 seconds.\r\n" );
document.write( "Adding on the first 20 minutes, 108 minutes, 14 2/17 seconds or\r\n" );
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document.write( "1 hour, 48 minutes, 14 2/17 seconds. \r\n" );
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document.write( "---------------------------\r\n" );
document.write( "---------------------------\r\n" );
document.write( "\r\n" );
document.write( "Now we'll bring in condition \"g\", which is also in three parts.\r\n" );
document.write( "For the first 20 minutes fill in As rate, 1/120, and\r\n" );
document.write( "20 minutes for the time \r\n" );
document.write( "Then fill in the \"tanks filled\" by multiplying rate by the time, getting \r\n" );
document.write( "20/120 or 1/6 of a tank filled.  \r\n" );
document.write( "For the next 20 minutes fill in A&B's rate, 1/120+1/150 = 3/200, and\r\n" );
document.write( "20 minutes for the time \r\n" );
document.write( "Then fill in the \"tanks filled\" by multiplying rate by the time, getting \r\n" );
document.write( "60/200 = 3/10 of a tank filled.\r\n" );
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document.write( "\r\n" );
document.write( "Then put x for the number of minutes after the\r\n" );
document.write( "first 40 minutes, and the sum of A's and B's rates \r\n" );
document.write( "1/120 + 1/150 = 3/200.\r\n" );
document.write( "Then to find the number of tanks filled we multiple the rate by the time,\r\n" );
document.write( "and get x/120  \r\n" );
document.write( "\r\n" );
document.write( "                               Number of      Time in       Rate in\r\n" );
document.write( "                               Tanks filled     minutes       tanks/hour\r\n" );
document.write( "       A only                        1            120         1/120\r\n" );
document.write( "       B only                        1            150         1/150\r\n" );
document.write( "       C only                       -1            180        -1/180\r\n" );
document.write( "g1. A only for 20 minutes           1/6            20         1/120 \r\n" );
document.write( "g2. A&B after 20 minutes           3/10            20         3/200\r\n" );
document.write( "g3. A only after 40 minutes       x/120             x         1/120\r\n" );
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document.write( "f1. A for 20 minutes                1/6            20          1/120 \r\n" );
document.write( "f2. A&B&C after 20 minutes    (17/1800)x            x        17/1800\r\n" );
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document.write( " We use\r\n" );
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document.write( "  , 64 minutes\r\n" );
document.write( "Adding on the first 40 minutes, 104 minutes or\r\n" );
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document.write( "1 hour, 44 minutes. \r\n" );
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document.write( "---------------------------\r\n" );
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document.write( "You do the last one!\r\n" );
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document.write( "Edwin

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