document.write( "Question 1190897: Sam jogged to Larry's house at 8 miles per hour and borrowed Larry's scooter, riding back at 20 miles per hour. If the round trip took 7 hours, how far is it to Larry's house? Write a distance equation \n" ); document.write( "
Algebra.Com's Answer #822624 by Theo(13342)\"\" \"About 
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rate * time = distance
\n" ); document.write( "for sam jogging:
\n" ); document.write( "rate * time = distance becomes 8 * x = distance
\n" ); document.write( "x = the time it took him to get to larry's home.
\n" ); document.write( "for sam riding back on larry's scooter:
\n" ); document.write( "rate * time = distance becomes 20 * y = distance.
\n" ); document.write( "y = the time it took him to get home.
\n" ); document.write( "your original two equations are:
\n" ); document.write( "8 * x = distance
\n" ); document.write( "20 * y = distance
\n" ); document.write( "the total time for the round trip was 7 hours.
\n" ); document.write( "this means that x + y = 7
\n" ); document.write( "solve for y to get:
\n" ); document.write( "y = 7 - x
\n" ); document.write( "the equations becomes:
\n" ); document.write( "for sam jogging:
\n" ); document.write( "8 * x = distance
\n" ); document.write( "for sam riding larry's scooter:
\n" ); document.write( "20 * (7 - x) = distance
\n" ); document.write( "your two equations are now:
\n" ); document.write( "8 * x = distance
\n" ); document.write( "20 * (7 - x) = distance
\n" ); document.write( "simplify the second equation and leave the first equation as is to get:
\n" ); document.write( "8 * x = distance
\n" ); document.write( "140 - 20 * x = distance
\n" ); document.write( "since distance = 8 * x in the first equation, replace distance with that in the second equation to get:
\n" ); document.write( "140 - 20 * x = 8 * x
\n" ); document.write( "add 20 * x to both sides to get:
\n" ); document.write( "140 = 28 * x
\n" ); document.write( "divide both sides by 28 to get:
\n" ); document.write( "5 = x
\n" ); document.write( "since x + y = 7, then y must be equal to 2.
\n" ); document.write( "your two original equations were:
\n" ); document.write( "8 * x = distance
\n" ); document.write( "20 * y = distance
\n" ); document.write( "replace x with 5 and y with 2 to get:
\n" ); document.write( "8 * 5 = 40
\n" ); document.write( "20 * 2 = 40
\n" ); document.write( "the distance is equal to 40 miles each way.
\n" ); document.write( "that would be a total of 80 miles round trip.
\n" ); document.write( "if you had added the distances together, then the round trip equation would have been:
\n" ); document.write( "8 * x + 20 * y = 80
\n" ); document.write( "with x = 5 and y = 2, the equation would have bvecome:
\n" ); document.write( "8 * 5 + 20 * 2 = 80
\n" ); document.write( "simplify to get:
\n" ); document.write( "40 + 40 = 80 which becomes 80 = 80, confirming the values of x and y are good.\r
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