document.write( "Question 213418: Bob leaves at 9am heading due north at 9mph. Tom leaves at 9:30am heading due south at 4mph. At what time will Bob and Tom be 10 miles apart? \n" ); document.write( "

Algebra.Com's Answer #161270 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
Bob leaves at 9am heading due north at 9mph. Tom leaves at 9:30am heading due south at 4mph. At what time will Bob and Tom be 10 miles apart?\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Bob traveled for one-half hour before Tom leaves at 9:30 am. Let this distance be d0=9*0.5=4.5 miles.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. So Total Distance traveled by Bob dBob=4.5+9t where t is the amount of time at which Bob and Tom are 10 miles apart.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Total Distance traveled by Tom is dTom = 4*t.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. But dBob+dTom = 10 miles\r
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\n" ); document.write( "\n" ); document.write( "Step 5. So substitute equation in Steps 2 and 3 into Step 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"4.5%2B9t%2B4%2At=10\"$ Solving this equation will yield the following steps:\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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This is an equation! Solutions: t=0.423076923076923.
Graphical form: Equation $\"4.5%2B9t%2B4%2At=10\"$ was fully solved.
Text form: 4.5+9t+4*t=10 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+4.5%2B9t%2B4%2At=10+%29\"$
For tutors: simplify_cartoon( 4.5+9t+4*t=10 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"highlight_red%28+4.5+%29%2B9%2At%2B4%2At=10\"$ .
Moved $\"4.5\"$ to the right of expression
It becomes $\"9%2At%2B4%2At%2Bhighlight_green%28+4.5+%29=10\"$ .
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Look at $\"highlight_red%28+9%2At+%29%2Bhighlight_red%28+4%2At+%29%2B4.5=10\"$ .
Eliminated similar terms $\"highlight_red%28+9%2At+%29\"$ , $\"highlight_red%28+4%2At+%29\"$ replacing them with $\"highlight_green%28+%289%2B4%29%2At+%29\"$
It becomes $\"highlight_green%28+%289%2B4%29%2At+%29%2B4.5=10\"$ .
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Look at $\"%28highlight_red%28+9+%29%2Bhighlight_red%28+4+%29%29%2At%2B4.5=10\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+13+%29%29%2At%2B4.5=10\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+13+%29%29%2At+%29%2B4.5=10\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+13+%29\"$
It becomes $\"highlight_green%28+13+%29%2At%2B4.5=10\"$ .
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Look at $\"13%2At%2B4.5=highlight_red%28+10+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-10+%29\"$
It becomes $\"13%2At%2B4.5-highlight_green%28+10+%29=0\"$ .
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Look at $\"13%2At%2Bhighlight_red%28+4.5+%29-highlight_red%28+10+%29=0\"$ .
Added fractions or integers together
It becomes $\"13%2At-highlight_green%28+55%2F10+%29=0\"$ .
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Look at $\"13%2At-highlight_red%28+55+%29%2Fhighlight_red%28+10+%29=0\"$ .
Factors 55 and 10 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes $\"13%2At-highlight_green%28+11+%29%2Fhighlight_green%28+2+%29=0\"$ .
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Look at $\"highlight_red%28+13%2At-11%2F2+%29=0\"$ .
Solved linear equation $\"highlight_red%28+13%2At-11%2F2=0+%29\"$ equivalent to 13*t-5.5 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: t=0.423076923076923.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "Step 6. t=0.42307 hours or t = 0.42307*60 minutes/hour = 25.42 minutes.\r
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\n" ); document.write( "\n" ); document.write( "Step 7. Time is therefore 9:30 am plus 25.42 minutes or 9:55 am.\r
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\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful.\r
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\n" ); document.write( "\n" ); document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r
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\n" ); document.write( "\n" ); document.write( "Good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J\r
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