document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209176>Question 1209176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man travels from A to B at 4 km/h and from B to A at 6 km/h. The total journey takes 45 minutes. Find the distance travelled. </SPAN>\n" );
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document.write( "Answer: <font color=red>3.6 km</font>\r<BR>\n" );
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document.write( "Work Shown\r<BR>\n" );
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document.write( "distance = rate*time<BR>\n" );
document.write( "d = r*t\r<BR>\n" );
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document.write( "Going from A to B<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "d = 4*t<BR>\n" );
document.write( "t = d/4\r<BR>\n" );
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document.write( "It takes d/4 hours to travel from A to B at a speed of 4 km/hr, where d is the distance from A to B.\r<BR>\n" );
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document.write( "Similar steps will show that it takes d/6 hours to travel from B to A at a speed of 6 km/hr.<BR>\n" );
document.write( "This assumes the person took the same route to go back to A, or they took a route of equal length. \r<BR>\n" );
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document.write( "The two time values must add to 45 minutes = 45/60 = 3/4 of an hour.<BR>\n" );
document.write( "Use the hour value because d/6 and d/4 are in hours.\r<BR>\n" );
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document.write( "(d/4) + (d/6) = 3/4<BR>\n" );
document.write( "12*( (d/4) + (d/6) ) = 12*(3/4)<BR>\n" );
document.write( "12*(d/4) + 12*(d/6) = 12*(3/4)<BR>\n" );
document.write( "3d + 2d = 9<BR>\n" );
document.write( "5d = 9<BR>\n" );
document.write( "d = 9/5<BR>\n" );
document.write( "d = 1.8 km exactly. This value hasn't been rounded.<BR>\n" );
document.write( "This is the one-way distance. <BR>\n" );
document.write( "The round trip distance is double that and it is 2*1.8 = <font color=red>3.6 km</font>\r<BR>\n" );
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document.write( "Another way to solve<BR>\n" );
document.write( "(d/4) + (d/6) = 3/4<BR>\n" );
document.write( "(3d/12) + (2d/12) = 3/4<BR>\n" );
document.write( "(3d+2d)/12 = 3/4<BR>\n" );
document.write( "5d/12 = 3/4<BR>\n" );
document.write( "5d*4 = 12*3<BR>\n" );
document.write( "20d = 36<BR>\n" );
document.write( "d = 36/20<BR>\n" );
document.write( "d = (9*4)/(5*4)<BR>\n" );
document.write( "d = 9/5<BR>\n" );
document.write( "d = 1.8 is the one-way distance; which doubles to a round trip distance of <font color=red>3.6 km</font>\r<BR>\n" );
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document.write( "Another approach is to convert each km per hr speed value into km per min.<BR>\n" );
document.write( "To do so, divide by 60.<BR>\n" );
document.write( "4 km per hr = 4/60 = 1/15 of a km per min<BR>\n" );
document.write( "6 km per hr = 6/60 = 1/10 of a km per min\r<BR>\n" );
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document.write( "Using d = r*t, we get this equation when going from A to B<BR>\n" );
document.write( "d = (1/15)*t<BR>\n" );
document.write( "which can be rearranged to<BR>\n" );
document.write( "t = 15d<BR>\n" );
document.write( "This is the time it takes, in minutes, to travel from A to B.\r<BR>\n" );
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document.write( "Similar steps will show it takes 10d minutes to travel from B to A.\r<BR>\n" );
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document.write( "Total travel time = 15d+10d = 25d = 45 min<BR>\n" );
document.write( "25d = 45<BR>\n" );
document.write( "d = 45/25<BR>\n" );
document.write( "d = (9*5)/(5*5)<BR>\n" );
document.write( "d = 9/5<BR>\n" );
document.write( "d = 1.8 km is the one-way distance which doubles to <font color=red>3.6 km</font> and it's the final answer.\r<BR>\n" );
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document.write( "Edit: tutor greenestamps makes a great point. I had a brainfart for some reason. My error has been fixed (changed the answer from 1.8 km to <font color=red>3.6 km</font>)<BR>\n" );
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