Question 42722
The working equation for this kind of problem is
t/A + t/B = 1
where t is the time worked together and A and B are individual times...
Here t = 2...if we let A be Winston's time, then Willie's time is A + 1...we have
2/A + 2/(A+1) = 1
Now multiply through by the LCD and solve...we get
2(A + 1) + 2A = A(A + 1)
2A + 2 + 2A = A^2 + A
A^2 - 3A - 2 = 0
This can't be factored so use the quadratic...
A = (3 ± sqrt(9 + 8)) / 2
A = (3 ± sqrt(17)) / 2
Since time can't be negative, Winston's time must be
(3 + sqrt(17)) / 2 or about 3.7 hours...