Question 825092
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rates:
x = maria
y = steph
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time = 1/rate
1/x = 1/y - 10
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working together rate:
x + y = 1/17
y = 1/17 - x
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1/x = 1/y - 10
1/x = 1/(1/17 - x) - 10
1/(1/17 - x) - 1/x = 10
x/x(1/17 - x) - (1/17 - x)/x(1/17 - x) = 10
x - (1/17 - x) = 10x(1/17 - x)
x - (1/17) + x = (10/17)x - 10xx
2x - (1/17) = (10/17)x - 10xx
-10xx - 2x + (10/17)x + (1/17) = 0
-10xx - (34/17)x + (10/17)x + (1/17) = 0
-10xx - (24/17)x + (1/17) = 0
-10xx - (1.411764705882353)x + (0.058823529411765) = 0
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the above quadratic equation is in standard form, with a=-10, b=-1.411764705882353, and c=0.058823529411765
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-10 -1.411764705882353 0.058823529411765
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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this quadratic has two real roots (the x-intercepts), which are:
x = -0.174823795
x = 0.0336473244
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the negative root does not fit the problem statement, so use the positive root
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rates:
x = 0.0336473244
y = 0.058823529411765 - 0.0336473244
y = 0.025176205011765
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answer:
times:
1/x = maria = 1/0.0336473244 = 29.7 hr
1/y = steph = 1/0.0251762050 = 39.7 hr
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Solve quadratic equations, quadratic formula:
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Solve systems of linear equations up to 6-equations 6-variables:
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