document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95836>Question 95836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your school is 18 3/4 miles south of Pittsburgh and your house is 44 1/4 miles south of Pittsburgh. You leave your school at 5:00 P.M., traveling south by bicycle at an average speed of 15 miles per hour. Your father leaves Pittsburgh in a car at 5:45 P.M. He is driving south at an average speed of 55 miles per hour. Let t represent the time it takes your father to drive from Pittsburgh toward your house.<BR>\n" );
document.write( "1. Find the time it would take you to ride your bicycle home.<BR>\n" );
document.write( "2. Find the time your father will arrive home.<BR>\n" );
document.write( "3. Write an equation to find your distance d1, from Pittsburgh after t hours.<BR>\n" );
document.write( "4. Write an equation to find your father's distance d2 from Pittsburgh after t hours.<BR>\n" );
document.write( "5. Use your equations from Exercises 3 and 4 to find how long it takes your father to pass you.<BR>\n" );
document.write( "6. Find the number of hours you rode your bicycle when your father passes you.<BR>\n" );
document.write( "7. At what time did your father pass you on your bicycle?<BR>\n" );
document.write( "8. How many miles did you ride your bicycle when your father passed you?<BR>\n" );
document.write( "9. You want to arrive home before your father. Assume that all other information stays the same. What time should you leave school?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69826 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=69826\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your school is 18 3/4 miles south of Pittsburgh and your house is 44 1/4 miles south of Pittsburgh. You leave your school at 5:00 P.M., traveling south by bicycle at an average speed of 15 miles per hour. Your father leaves Pittsburgh in a car at 5:45 P.M. He is driving south at an average speed of 55 miles per hour. Let t represent the time it takes your father to drive from Pittsburgh toward your house.<BR>\n" );
document.write( "1. Find the time it would take you to ride your bicycle home.<BR>\n" );
document.write( "t = d/r; t=(44 1/4 - 18 3/4)/15 = 25.5/15 = 1.7 hrs<BR>\n" );
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document.write( "2. Find the time your father will arrive home.<BR>\n" );
document.write( "t = d/r; t= [44 1/4] /55 =0.804545... hrs <BR>\n" );
document.write( "0.804544*60 *60 min = 48.27 minutes<BR>\n" );
document.write( "5:45 + 48.27 min = 6:33\r<BR>\n" );
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document.write( "3. Write an equation to find your distance d1, from Pittsburgh after t hours.<BR>\n" );
document.write( "d1 =18.75 + 15t<BR>\n" );
document.write( "4. Write an equation to find your father's distance d2 from Pittsburgh after t hours.<BR>\n" );
document.write( "d2 = 55t<BR>\n" );
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document.write( "5. Use your equations from Exercises 3 and 4 to find how long it takes your father to pass you.<BR>\n" );
document.write( "Son leaves school 45 minutes before father leaves Pittsburgh.\r<BR>\n" );
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document.write( "d1 = 18.75 + 15(t+(3/4))<BR>\n" );
document.write( "d2 = 55t<BR>\n" );
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document.write( "Father passes son when there distances from Pittsburg are the same:<BR>\n" );
document.write( "55t = 18.75+15t+15*(3/4)<BR>\n" );
document.write( "40t = 18.75+11.25<BR>\n" );
document.write( "40t = 30 <BR>\n" );
document.write( "t = 3/4 hr or 45 minutes<BR>\n" );
document.write( "Father will pass Son after Father has been on the road 45 minutes.<BR>\n" );
document.write( "That's at 6:30<BR>\n" );
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document.write( "Find the number of hours you rode your bicycle when your father passes you.<BR>\n" );
document.write( "45 min + 45 min = 1 1/2 hrs.<BR>\n" );
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document.write( "7. At what time did your father pass you on your bicycle?<BR>\n" );
document.write( "6:30<BR>\n" );
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document.write( "8. How many miles did you ride your bicycle when your father passed you?<BR>\n" );
document.write( "(3/2)hr*15 mph = 22 1/2 miles<BR>\n" );
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document.write( "9. You want to arrive home before your father. Assume that all other information stays the same. What time should you leave school?<BR>\n" );
document.write( "To get there the same time father travels 44.25 miles when son travels<BR>\n" );
document.write( "44.25-18.75 mi = 25.5 miles distance son goes; 44.25= distance father goes\r<BR>\n" );
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document.write( "Son time from 5:00 = 25.5/15 = 1.7 hrs <BR>\n" );
document.write( "Father time = 44.25/55 = 0.804545 hrs from 5:45<BR>\n" );
document.write( "Adding the 0.75 hr to the father's time he took 1.5545 hrs from 5:00<BR>\n" );
document.write( "Difference is 1.7-1.5545 = 0.1455 hrs or 8.73 minutes<BR>\n" );
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document.write( "Son need to leave school more than 8.73 minutes earlier.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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