SOLUTION: As an example of a real life problem that requires rational expressions to solve, you may want to know how much of a 25% alcohol solution you need to add to 1L of water to produce

Question 184284: As an example of a real life problem that requires rational expressions to solve, you may want to know how much of a 25% alcohol solution you need to add to 1L of water to produce a 10% alcohol solution.
As another example of a problem that requires rational expressions, if you know that John can finish a job in one hour and Sally can finish it in two hours, you may want to know how long will it take to finish the job if both are working together.
Please help me solve these.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
As an example of a real life problem that requires rational expressions to solve, you may want to know how much of a 25% alcohol solution you need to add to 1L of water to produce a 10% alcohol solution.
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Note: Call the alcohol in the diluted mixtures "alcohol".
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Equation:
alcohol + alcohol = alcohol
0.25x + 0*1 L = 0.10(x+1)
Multiply thru by 100 to get:
25x + 0 = 10x + 10
15x = 10
x = 2/3 Liter (amt. of 25% solution in the mixture)
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As another example of a problem that requires rational expressions, if you know that John can finish a job in one hour and Sally can finish it in two hours, you may want to know how long will it take to finish the job if both are working together. -
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Equation:
rate + rate = together rate
1/1 + 1/2 = 1/x
Multiply thru by 2x to get
2x + x = 2
3x = 2
x = 2/3 hr. (time to do the job together)
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Cheers,
Stan H.

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