Quizzes & Puzzles66 mins ago
Math question...
2 Answers
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?
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?
Answers
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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)
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)
1 to 2 of 2
