X,Y and Z can do a piece of work in 15 days. If X takes twice as much as Y and Z together and Y takes thrice as much as X and Z together, how long days will each take to finish a work.

Answer 1

Time=1work/rate

a) 15=1/(X+Y+Z)
b) 2(Y+Z)=X
c) 2(X+Z)=Y

putting them into matrix form
a) X+Y+Z=1/15
b) X-2Y-2Z=0
c) 2X-Y+2Z=0

adding the last two equation
3X-3Y=0 or X=Y
mulitplying a) by 2, and adding it to b)
3x=2/15
X=2/45 or X can do one each 22.5 days, and
then y=2/45 so Y can do one each 22.5 days
you solve for Z

Answer 2

Find two separate equation of x^2+2xy+y^2-2x-2y-15=0

Answer 3

(x+y)^2 - 2(x+y) - 15 = 0
(x+y-5)(x+y+3) = 0
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