document.write( "Question 370575: Liz commutes 30 mi. to her job each day. She Finds that if she drives 10 mi/h faster it takes her 6 minutes less to get to work. Find her new speed.\r
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document.write( "I tried setting this problem up on a chart. For some reason when I worked the problem out I came out with really odd fractions, and I am not quite sure what I have done wrong. Any kind of help would truly mean a lot to me. \n" );
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Algebra.Com's Answer #264133 by jim_thompson5910(35256)![]() ![]() ![]() You can put this solution on YOUR website! Let r = original speed.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "and let t = time to get to work driving that original speed.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So if \"Liz commutes 30 mi. to her job each day\", this means that \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So the first equation is \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "In addition, because \"she drives 10 mi/h faster it takes her 6 minutes less to get to work\", we can say that \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Notes: since she drives 10 mph faster, her new speed is r+10. Also, because 60 min = 1 hour, this means that 6 min = \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So the second equation is \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "-----------------------------------------------------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Now let's use both equations to solve for t and r\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Note: the 't' terms cancel in the first fraction while in the second, we're dividing each term by 10.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Notice that the quadratic \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for \"t\":\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So the possible solutions are \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "However, since a negative time isn't possible, this means that the only solution for 't' is \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Remember that 't' is the time in hours. So convert to minutes to get \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So the time it takes to travel 30 miles at the original speed is 36 minutes.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Recall that we made \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So her original speed is 50 mph. Add 10 mph to this speed to get 50+10 = 60 mph\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So her new speed is 60 mph.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "I'll leave the check to you. Remember to use the formula \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Also, feel free to check out my tutoring website\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( " |