document.write( "Question 115714: Two boats pass each other going in opposite directions. The first boat travels 2 miles per hour faster than the second boat. What is the average speed of each boat if they are 6 miles apart after 2 hours? \n" ); document.write( "

Algebra.Com's Answer #84255 by ptaylor(2198) $\"\"$ $\"About$

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Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r\r
\n" ); document.write( "\n" ); document.write( "Let r=rate (speed) of second boat
\n" ); document.write( "Then r+2=rate of first boat\r
\n" ); document.write( "\n" ); document.write( "Now we know that after the boats pass, they are separating at the rate of (r+(r+2)) mph (Note: Another way to look at this problem is as follows: In two hours, second boat travels 2r mi and the first boat travels 2(r+2) mi. Now we know that these two distances equals 6 mi so 2r+2(r+2)=6 ---divide both sides by 2 and we get the same equation as below)\r
\n" ); document.write( "\n" ); document.write( "So our equation to solve is:\r
\n" ); document.write( "\n" ); document.write( "r+r+2=6/2 or------------------------(rate=dist/time)
\n" ); document.write( "r+r+2=3 subtract 2 from both sides
\n" ); document.write( "r+r+2-2=3-2 collect like terms\r
\n" ); document.write( "\n" ); document.write( "2r=1 divide both sides by 2
\n" ); document.write( "r=1/2 mph-----------------------speed of second boat
\n" ); document.write( "r+2=(1/2)+2=2 1/2 mph-----------------speed of first boat\r
\n" ); document.write( "\n" ); document.write( "CK
\n" ); document.write( "In two hours, the second boat travels 2*(1/2) or 1 mi
\n" ); document.write( "In two hours, the second boat travels 2*(2 1/2) or 5 mi\r
\n" ); document.write( "\n" ); document.write( "5+1=6
\n" ); document.write( "6=6\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor \n" ); document.write( "

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