document.write( "Question 769626: Please help me and provide explanation to understand further,\r
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\n" ); document.write( "\n" ); document.write( "Because of bad weather, a bus driver reduced the usual speed along a 150-mile bus route by 10 mph. The bus arrived only 30 minutes later than its usual arrival time. How fast does the bus usually travel? \n" ); document.write( "
Algebra.Com's Answer #468958 by ramkikk66(644)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Because of bad weather, a bus driver reduced the usual speed along a 150-mile bus route by 10 mph. The bus arrived only 30 minutes later than its usual arrival time. How fast does the bus usually travel?\r\n" );
document.write( "Ans:\r\n" );
document.write( "Let the bus' normal speed be x mph.\r\n" );
document.write( "Normal time taken to cover 150 miles = 150/x hours (since time = distance / speed)\r\n" );
document.write( "If he reduces the speed by 10 mph, the new speed = x - 10\r\n" );
document.write( "Time taken at the slower speed = 150/(x - 10) hours\r\n" );
document.write( "It is given that the new time is 0.5 hours (30 minutes) more than the normal \r\n" );
document.write( "time.\r\n" );
document.write( "So we get the equation\r\n" );
document.write( "\"150%2F%28x+-+10%29+=+150%2Fx+%2B+0.5\"\r\n" );
document.write( "\"150%2Ax+=+150%2A%28x+-+10%29+%2B+0.5%2Ax%2A%28x+-+10%29\"\r\n" );
document.write( "\"150%2Ax+=+150%2Ax+-+1500+%2B+0.5%2Ax%5E2+-+5%2Ax\"\r\n" );
document.write( "\"0.5%2Ax%5E2+-+5%2Ax+-+1500+=+0\" or\r\n" );
document.write( "\"x%5E2+-+10%2Ax+-+3000+=+0\"\r\n" );
document.write( "This is a standard quadratic equation which can be solved through factorization\r\n" );
document.write( "\"%28x+-+60%29%2A%28x+%2B+50%29+=+0\"\r\n" );
document.write( "The two solutions are:\r\n" );
document.write( "x - 60 = 0 i.e. x = 60\r\n" );
document.write( "x + 50 = 0 i.e. x = -50\r\n" );
document.write( "Since x cannot be negative, x = 60\r\n" );
document.write( "Normal speed = \"highlight%2860%29\" mph\r\n" );
document.write( "Check for correctness:\r\n" );
document.write( "At normal speed, time taken = 150/60 = 2.5 hours\r\n" );
document.write( "Reduced speed = 60 - 10 = 50\r\n" );
document.write( "Time taken at 50 mph = 150/50 = 3 hours which is 30 minutes more than 2.5 hrs!\r\n" );
document.write( "So the answer is correct. Hope you got it :)\r\n" );
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