document.write( "Question 472725: 1.) Jonathan drove his car from A to B at 81 km/hr. His car broke down and he returned by bus at 54 km/hr. his total travel was 5 hours. how long was his trip by car? \n" ); document.write( "
Algebra.Com's Answer #324072 by Theo(13342)\"\" \"About 
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his car presumably broke down when he was at B.
\n" ); document.write( "the formula to use for this type of problem is rate * time = distance.
\n" ); document.write( "let the distance between A and B equal d.
\n" ); document.write( "the time it took to get there and back = 5.
\n" ); document.write( "the rate to get there is 81 k/m.
\n" ); document.write( "the rate to get back is 54 k/m.
\n" ); document.write( "let h1 equal the hours it took to get there.
\n" ); document.write( "let h2 equal the hours it took to get back.
\n" ); document.write( "the rate * time formula to go from A to B is:
\n" ); document.write( "81 * h1 = d
\n" ); document.write( "the rate * time formula to go from B to A is:
\n" ); document.write( "54 * h2 = d
\n" ); document.write( "since they are both equal to d, then we can set each of these equations equal to each other, so we get:
\n" ); document.write( "81 * h1 = 54 * h2
\n" ); document.write( "we also know that:
\n" ); document.write( "h1 + h2 = 5
\n" ); document.write( "we can substitute for h1 by solving the equation for h1 by getting:
\n" ); document.write( "h1 = 5 - h2
\n" ); document.write( "substituting in the equation of:
\n" ); document.write( "81 * h1 = 54 * h2 gets us:
\n" ); document.write( "81 * (5 - h2) = 54 * h2
\n" ); document.write( "simplifying gets us:
\n" ); document.write( "(81 * 5) - (81 * h2) = (54 * h2)
\n" ); document.write( "adding (81 * h2) to both sides of this equation gets:
\n" ); document.write( "81 * 5 = (54 * h2) + (81 * h2) which becomes:
\n" ); document.write( "81*5 = 135*h2
\n" ); document.write( "dividing both sides of this equation by 135 gets:
\n" ); document.write( "h2 = 81*5/135 which becomes:
\n" ); document.write( "h2 = 3
\n" ); document.write( "this means that h1 = 2 because h1 + h2 = 5
\n" ); document.write( "we have:
\n" ); document.write( "h1 = 2
\n" ); document.write( "h2 = 3
\n" ); document.write( "it took 2 hours to get there by car.
\n" ); document.write( "it took 3 hours to get back by bus.
\n" ); document.write( "plug into rate * time = distance formula to get:
\n" ); document.write( "81 * 2 = 162
\n" ); document.write( "54 * 3 = 162
\n" ); document.write( "the distance was 162 kilometers each way.
\n" ); document.write( "the total travel time was 5 hours.
\n" ); document.write( "answer to the question is that the trip by car took 2 hours.\r
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