Question 632365
Working together, two people can complete a task in 8 hours. Working alone, one person takes 2 hours longer than the other to complete the task. How long would it take for each person to complete the task? (Round your answers to one decimal place.)
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Let x = time (hours) it takes one person
then
x+2 = time (hours) it takes second person
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8(1/x + 1/(x+2)) = 1
multiplying both sides by x(x+2):
8(x+2 + x) = x(x+2)
8(2x+2) = x^2+2x
16x+16 = x^2+2x
16 = x^2-14x
0 = x^2-14x-16
since we can't factor we 
apply "quadratic formula" to get:
x = {15.1, -1.1}
throw out the -1.1 (extraneous) leaving:
x = 15.1 hours (one person's time)
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second person's time:
x+2 = 15.1+2 = 17.1 hours 
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Answer: 15.1 hours and 17.1 hours
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details of quadratic formula:
*[invoke quadratic "x", 1, -14, -16 ]