document.write( "Question 156928: A bus traveled 2 hours at a certain speed, then decreased the speed by 20 miles/hr and traveled for 3 more hours. If the total distance traveled is estimated between 250 miles and 330 miles, find the range of the initial speed of the bus. \n" ); document.write( "
Algebra.Com's Answer #115714 by gonzo(654)![]() ![]() ![]() You can put this solution on YOUR website! bus traveled 2 hours at x miles per hour. \n" ); document.write( "bus traveled 3 hours at (x-20) miles per hour. \n" ); document.write( "total distance was between 250 and 330 miles. \n" ); document.write( "solve each separately. \n" ); document.write( "rate * time = distance, so ... \n" ); document.write( "250 = 2*x + 3*(x-20) = 2*x + 3*x - 60. \n" ); document.write( "310 = 5*x (add 60 to both sides of the equation to eliminate the 60 from the right hand side). \n" ); document.write( "x = 62 miles per hour. \n" ); document.write( "bus traveled 2 hours at 62 miles per hour and 3 hours at 42 miles per hour. \n" ); document.write( "calculating out at these rates yields 124 + 126 = 250 so the answer checks out. \n" ); document.write( "that's the low end. \n" ); document.write( "the high end is as follows: \n" ); document.write( "330 = 2.x + 3.(x-20) = 2*x + 3*x - 60. \n" ); document.write( "390 = 5*x (add 60 to both sides of the equation to eliminate the 60 from the right hand side). \n" ); document.write( "x = 78 miles per hour. \n" ); document.write( "bus traveled 2 hours at 78 miles per hour and 3 hours at 58 miles per hour. \n" ); document.write( "calculating out yields 156 + 174 = 330 so the answer checks out. \n" ); document.write( "final answer is: \n" ); document.write( "bus travels between 62 miles per hour and 78 miles per hour for 2 hours and then travels between 42 miles per hour and 58 miles per hour for 3 hours. \n" ); document.write( " |