document.write( "Question 1011058: . to travel from singapore to kuala lampur ,a distance kf 390km , motoridt finds that if he travels 6 km/h faster than its usual average speed,he will take 15 minutes less ti complete his usual journey . Calculate the usual avergae speed of the motorist \n" ); document.write( "

Algebra.Com's Answer #626597 by josgarithmetic(39617) $\"\"$ $\"About$

You can put this solution on YOUR website!
This form of travel rates problem is common as an exercise.\r
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document.write( "           rate     time      distance\r\n" );
document.write( "IF         r+6      t-1/4      390\r\n" );
document.write( "Usual      r        t          390\r\n" );
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document.write( "           rate     time      distance\r\n" );
document.write( "IF         r+k      t-h        d\r\n" );
document.write( "Usual      r        t          d\r\n" );
document.write( "

\n" ); document.write( "Be sure you understand what is happening in and between the two data tables above.\r
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\n" ); document.write( "\n" ); document.write( " $\"system%28%28r%2Bk%29%28t-h%29=d%2Crt=d%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"rt%2Bkt-hr-hk=d\"$
\n" ); document.write( " $\"d%2Bkt-hr-hk=d\"$
\n" ); document.write( " $\"kt-hr-hk=0\"$
\n" ); document.write( " $\"kt=hr-hk\"$
\n" ); document.write( " $\"t=%28hr-hk%29%2Fk\"$ ------formula for t in terms of r\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"rt=d\"$
\n" ); document.write( " $\"r=d%2Ft\"$
\n" ); document.write( " $\"r=d%2A%281%2Ft%29\"$
\n" ); document.write( " $\"r=d%28k%2F%28hr-hk%29%29\"$
\n" ); document.write( " $\"r%28hr-hk%29=dk\"$
\n" ); document.write( " $\"highlight_green%28hr%5E2-hkr-dk=0%29\"$ -----quadratic equation in the unknown variable, r.
\n" ); document.write( "You can use the formula for general solution of a quadratic equation and try to simplify
\n" ); document.write( "that, if at all possible, ... or you can simply substitute the given, known values for h
\n" ); document.write( ", k, and d, now and then deal with the resulting form of quadratic equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"%281%2F4%29r%5E2-%281%2F4%29%2A6r-390%2A6=0\"$
\n" ); document.write( " $\"%281%2F4%29r%5E2-%283%2F2%29r-2340=0\"$
\n" ); document.write( " $\"highlight_green%28r%5E2-6r-9360=0%29\"$ ----now the quadratic equation is less general, fewer symbols.\r
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\n" ); document.write( "\n" ); document.write( " $\"r=%286%2B-+sqrt%2836%2B4%2A9360%29%29%2F2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"r=%286%2B-+sqrt%2837476%29%29%2F2\"$
\n" ); document.write( " $\"r=%286%2B-+sqrt%284%2A9%2A3%2A347%29%29%2F2\"$
\n" ); document.write( " $\"r=%286%2B-+2%2A3sqrt%283%2A347%29%29%2F2\"$ ----you need the PLUS form.
\n" ); document.write( " $\"highlight%28r=3%2B3sqrt%283%2A347%29%29\"$
\n" ); document.write( "Do whatever you need with this value.\r
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\n" ); document.write( "\n" ); document.write( "--
\n" ); document.write( "347 and 3 both are prime numbers. Decimal approximate for the solution is $\"highlight%28r=99.8%29\"$ . \n" ); document.write( "

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