Math question...

[ameriland]

An apprentice builds a machine, it takes him 15 hours longer as the master.
If both work together they are finished 5 hours earlier than when the master does it alone.
How long does it take for the master to build the machine on his own?

[keyplus90]

12.5 hrs

[jake-the-peg]

OK this is a little complex
say
Time for the master = x
Time for apprentice = y
so y=15+x (you probably got that far)

The rate the apprentice can build machines at is Ra = 1/y
The rate the master can build machines at is Rm = 1/x

The rate they can both build them at = Ra+Rm= 1/y + 1/x

so the time taken to build 1 is 1/ (1/y+ 1/x) which = x-5

so 1/(x-5) = 1/y+1/x

as y=15+x (above)

1/(x-5) =1/(x+15) +1/x = x+(x+15) / x(x+15)

so x(x+15) = (x-5)(2x+15)

if you multiply that out you'll get a quadratic equation that you can simply solve for x

x�-10x-75=0

which I make a bit under 16 hours

You'll want to get the proper answer and check I haven't done anything daft (It has been known)