SOLUTION: Hello! I’m having some difficulty figuring out how to solve this question step-by-step. Any help is appreciated! Working together, Julie and Kendra can pick forty bushels of

Algebra ->  Rational-functions -> SOLUTION: Hello! I’m having some difficulty figuring out how to solve this question step-by-step. Any help is appreciated! Working together, Julie and Kendra can pick forty bushels of       Log On


   

Question 1158434: Hello! I’m having some difficulty figuring out how to solve this question step-by-step. Any help is appreciated!
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. 
Found 2 solutions by Boreal, Shin123:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
in 1 hour, Julie picks 1/9, and Kendra picks 1/x, x not being known.
together they do (1/4.95) per hour
(1/9)+(1/x) =1/4.95
multiply both sides by 9x(4.95)
4.95x+44.55=9x
4.05x=44.55
x=11 hours
so in 1 hour they pick (1/9) and (1/11) of the total, which is 20/99 of the total
in 4.95 hours, they pick the whole 99/99

Answer by Shin123(626) About Me  (Show Source):
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.
Solved by pluggable solver: Solve an equation
This is a solution to the equation:
Your Result:


YOUR ANSWER


  • 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.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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.
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
This is an equation! Solutions: x=11.

Universal Simplifier and Solver


Done!
0=0;x=11
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:
Solved by pluggable solver: Solveing rate of work problems


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.