document.write( "Question 1158434: Hello! I’m having some difficulty figuring out how to solve this question step-by-step. Any help is appreciated! \r
\n" ); document.write( "\n" ); document.write( "Working together, Julie and Kendra can pick forty bushels of apples in 4.95 hours. Had she done it alone it would have taken Julie 9 hours. Find how long it would take Kendra to do it alone. \n" ); document.write( "

Algebra.Com's Answer #781388 by Shin123(626) $\"\"$ $\"About$

You can put this solution on YOUR website!
Suppose it takes x hours for Kendra to do it alone. In 1 hour, Julie can complete $\"1%2F9\"$ of the job. In 1 hour, Kendra can complete $\"1%2Fx\"$ of the job. They can complete $\"1%2F9%2B1%2Fx\"$ of the job in 1 hour together. $\"1%2F9%2B1%2Fx=x%2F9x%2B9%2F9x=%28x%2B9%29%2F9x\"$ . Therefore, it takes them $\"9x%2F%28x%2B9%29\"$ hours to do the job together. So we have $\"4.95=9x%2F%28x%2B9%29\"$ Multiplying both sides by x+9 gives $\"4.95%28x%2B9%29=9x\"$ . Expanding gives $\"4.95x%2B44.55=9x\"$ . \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Solved by pluggable solver: Solve an equation

This is a solution to the equation:
Your Result:

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This is an equation! Solutions: x=11.
Graphical form: Equation $\"4.95x%2B44.55=9x\"$ was fully solved.
Text form: 4.95x+44.55=9x simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+4.95x%2B44.55=9x+%29\"$
For tutors: simplify_cartoon( 4.95x+44.55=9x )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"4.95%2Ax%2B44.55=highlight_red%28+9%2Ax+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-9%2Ax+%29\"$
It becomes $\"4.95%2Ax%2B44.55-highlight_green%28+9%2Ax+%29=0\"$ .
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Look at $\"4.95%2Ax%2Bhighlight_red%28+44.55+%29-9%2Ax=0\"$ .
Moved $\"44.55\"$ to the right of expression
It becomes $\"4.95%2Ax-9%2Ax%2Bhighlight_green%28+44.55+%29=0\"$ .
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Look at $\"highlight_red%28+4.95%2Ax+%29-highlight_red%28+9%2Ax+%29%2B44.55=0\"$ .
Eliminated similar terms $\"highlight_red%28+4.95%2Ax+%29\"$ , $\"highlight_red%28+-9%2Ax+%29\"$ replacing them with $\"highlight_green%28+%284.95-9%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%284.95-9%29%2Ax+%29%2B44.55=0\"$ .
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Look at $\"%28highlight_red%28+4.95+%29-highlight_red%28+9+%29%29%2Ax%2B44.55=0\"$ .
Added fractions or integers together
It becomes $\"%28-highlight_green%28+405%2F100+%29%29%2Ax%2B44.55=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+405%2F100+%29%29%2Ax+%29%2B44.55=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+405+%29\"$ , $\"highlight_red%28+1%2F100+%29\"$
It becomes $\"-highlight_green%28+405+%29%2Fhighlight_green%28+100+%29%2Ax%2B44.55=0\"$ .
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Look at $\"-highlight_red%28+405+%29%2Fhighlight_red%28+100+%29%2Ax%2B44.55=0\"$ .
Factors 405 and 100 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes $\"-highlight_green%28+81+%29%2Fhighlight_green%28+20+%29%2Ax%2B44.55=0\"$ .
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Look at $\"highlight_red%28+-81%2F20%2Ax%2B44.55+%29=0\"$ .
Solved linear equation $\"highlight_red%28+-81%2F20%2Ax%2B44.55=0+%29\"$ equivalent to -4.05*x+44.55 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
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Universal Simplifier and Solver

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Done!
0=0;x=11

\n" ); document.write( " Subtracting 44.55 from both sides gives $\"-4.05x=-44.55\"$ . Dividing both sides by -4.05 gives $\"x=11\"$ . So it takes Kendra 11 hours to do it alone. Check using this solver: \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

Solved by pluggable solver: Solveing rate of work problems

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\n" ); document.write( "It takes you 9 hours and it takes your friend 11 hours. So you complete $\"1%2F9\"$ of the puzzle in a hour and your friend completes $\"1%2F11\"$ of the puzzle in a hour. And $\"1%2F9%2B1%2F11=0.202020202020202\"$ So it is going to take you and your friend just $\"1%2F0.202020202020202=highlight%284.95%29\"$ hours to do the puzzle together.\r
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