document.write( "Question 122253: The total distance was 540 miles. Part of the joureny was on a motorcylce at 40 mph and PART WAS IN A CAR AT 60 Mph. What distance was covered by motorcycle if the total time of the journey was 11 hours? \n" ); document.write( "

Algebra.Com's Answer #89774 by solver91311(24713) $\"\"$ $\"About$

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document.write( "The basic formula is .\r
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document.write( "Let's call the distance travelled by the motorcycle , the
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document.write( "motorcycle's rate , and the time spent on the motorcycle .
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document.write( "Hence, for the motorcycle part of the trip we have .
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document.write( "Since we are given the motorcycle's speed, we can write .\r
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document.write( "Likewise for the car part of the trip we have , and
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document.write( "substituting the given speed we have .\r
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document.write( "We also know that the total distance is 540 miles, so we can say:
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document.write( "And we know that the total time is 11 hours, so we can say:
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document.write( "From here we need to find a way to express a relationship that is an equation
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document.write( "in one variable.\r
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document.write( " =>  and
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document.write( "  => \r
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document.write( "Next we can substitute these two expressions for  and 
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document.write( "into the equation that we developed to describe the car part of the trip, thus:\r
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document.write( "Simplifying and collecting like terms gives us:
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document.write( "Recalling the equation that we developed for the motorcycle part of the trip:
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document.write( ", we now have two different expressions for  in terms of  that we can equate, since .\r
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document.write( "Solving:\r
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document.write( "Now we know that the motorcycle part of the trip took 6 of the 11 hours total
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document.write( "time.  Substituting this value into the original equation for the motorcycle
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document.write( "portion we get:\r
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document.write( "Giving us 240 miles for the distance traveled by motorcycle.\r
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document.write( "Check the answer\r
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document.write( "The car part of the trip must have taken  hours, so the car
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document.write( "distance must have been  miles.\r
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document.write( " which was the given total distance.  Answer checks. \n" );
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