document.write( "Question 55446: here i am again... plz help m regarding this problem...thanks a lot!!
\n" ); document.write( "19.Rose drove her car from her home to the province and back, a total distance of 120km. Her average speed returning was 3kph slower than her average speed going to the province. If her total driving time was 9 hours, what was her average speed in going to the province?\r
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Algebra.Com's Answer #37619 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
19.Rose drove her car from her home to the \r\n" );
document.write( "province and back, a total distance of 120km. Her \r\n" );
document.write( "average speed returning was 3kph slower than her \r\n" );
document.write( "average speed going to the province. If her total \r\n" );
document.write( "driving time was 9 hours, what was her average speed \r\n" );
document.write( "in going to the province? thanks a lot tutorz!!\r\n" );
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document.write( "Rose drove very slowly to have taken 9 hours to travel \r\n" );
document.write( "only 120km. I will assume the traffic was extremely \r\n" );
document.write( "heavy both ways.\r\n" );
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document.write( "The words \"a total distance of 120km\" are ambiguous.  Is \r\n" );
document.write( "it 60km going and 60km returning for a total of 120km?  \r\n" );
document.write( "Or is the total distance between her home and the province \r\n" );
document.write( "120km?  Either way she is still driving very slowly.\r\n" );
document.write( "I will assume she is driving the slowest and the distance\r\n" );
document.write( "between her home and the province is 60km.\r\n" );
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document.write( "Make this chart:\r\n" );
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document.write( "             DISTANCE    RATE      TIME\r\n" );
document.write( "Going                                      \r\n" );
document.write( "Returning                                    \r\n" );
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document.write( "Fill in the two distances, which are both 60:\r\n" );
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document.write( "             DISTANCE    RATE      TIME\r\n" );
document.write( "Going          60                       \r\n" );
document.write( "Returning      60                           \r\n" );
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document.write( "Since the question is\r\n" );
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document.write( ">>...what was her average speed in going to the province...<<\r\n" );
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document.write( "We will let x represent her speed going, so we fill in x for \r\n" );
document.write( "the rate going:\r\n" );
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document.write( "             DISTANCE    RATE      TIME\r\n" );
document.write( "Going          60          x             \r\n" );
document.write( "Returning      60                                  \r\n" );
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document.write( ">>...Her average speed returning was 3kph slower...<<\r\n" );
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document.write( "3kph slower than x kph is x-3 kph. So we fill that in for the \r\n" );
document.write( "rate returning:\r\n" );
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document.write( "             DISTANCE    RATE      TIME\r\n" );
document.write( "               60          x                               \r\n" );
document.write( "Returning      60         x-3              \r\n" );
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document.write( "Now we use the fact that TIME = DISTANCE/RATE to fill in the \r\n" );
document.write( "times:\r\n" );
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document.write( "             DISTANCE    RATE      TIME\r\n" );
document.write( "Going          60          x       60/x\r\n" );
document.write( "Returning      60         x-3     60/(x-3)\r\n" );
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document.write( "To find the equation we use this:\r\n" );
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document.write( ">>...her total driving time was 9 hours...<<\r\n" );
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document.write( "We add the two TIME's and put that equal to 9\r\n" );
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document.write( "60/x + 60/(x-3) = 9\r\n" );
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document.write( "Can you solve that by first multiplying through by \r\n" );
document.write( "LCD = x(x-3) ? If not post again.\r\n" );
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document.write( "You will get two answers: x = 16 and x = 4/3\r\n" );
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document.write( "We must discard the 4/3, since that would cause her\r\n" );
document.write( "rate returning to be negative.  So the answer is\r\n" );
document.write( "a very slow 16 kph.\r\n" );
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document.write( "If we assume it was 120km from her home to the\r\n" );
document.write( "province the equation is not factorable and the\r\n" );
document.write( "answer is 28.251 kph, which is still very slow.\r\n" );
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document.write( "Edwin
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