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Question 929993: Working together, Rosa and Dianne can plant 20 flats of pansies in 3 hours. If Rosa works alone, it takes her 8 hours longer than it takes Dianne alone to plant all 20 flats. How long does it take Rosa to plant the pansies by herself?
Found 2 solutions by ewatrrr, TimothyLamb:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! amount per hour KEY
 |Multiplying thru by 24x so as all denominators = 1
3x + 24 = 8x
24 = 5x
24/5 hr = x = 4.8hr, time it takes Rosa to plant the pansies by herself
and...checking
1/8 + 1/(24/5) = 3/24 + 5/24 = 8/24 = 1/3
Answer by TimothyLamb(4379)  (Show Source):
You can put this solution on YOUR website! x = rosa rate
y = dianne rate
t = time for dianne to plant 20 flats
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r = w/t
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x = 1/(t + 8)
y = 1/t
x + y = 1/3
1/(t + 8) + 1/t = 1/3
t/t(t + 8) + (t + 8)/t(t + 8) = 1/3
t + (t + 8) = (1/3)*t(t + 8)
2t + 8 = (1/3)tt + (8/3)t
(1/3)tt + (8/3)t - 2t - 8 = 0
(1/3)tt + (8/3)t - (16/3)t - 8 = 0
(1/3)tt - (8/3)t - 8 = 0
0.33333tt - 2.66666t - 8 = 0
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the above quadratic equation is in standard form, with a=0.33333, b=-2.66666 and c=-8
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
0.33333 -2.66666 -8
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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t = 10.3246233
t = -2.32456327
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the negative root doesn't fit the problem statement, so use the positive root:
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t = 10.3246233
t + 8 = 18.3246233
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answer:
time for rosa to plant 20 flats = 18.3 hours
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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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