Word Problem confusion

Linear spaces and subspaces, linear transformations, bases, etc.
doublechekk
Posts: 1
Joined: Sat Oct 22, 2016 12:09 am
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Word Problem confusion

Hi,
I have what I hope to be a dumb question. I just need to ensure I have the equation correct.

a, b, c build houses. Each house can be build in the following ways:
a and b work together for 6 hours and c works for 4 hours
a and b work together for 2 hours and c works for 8 hours
a works alone for 3 hours, b works alone for 1 hour and z works together for two hours

with a and b working together I'm confused on how to setup the equation

(x+y=6)+4z=1
(x+y=2)+8z=1
3x +1y + 2z =1

Any help would be appreciated.

buddy
Posts: 197
Joined: Sun Feb 22, 2009 10:05 pm
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Re: Word Problem confusion

I just need to ensure I have the equation correct.

A, B, and C build houses. Each house can be build in the following ways:

i) A and B work together for 6 hours, and C works for 4 hours
ii) A and B work together for 2 hours, and C works for 8 hours
iii) A works alone for 3 hours, B works alone for 1 hour, and Z works together for two hours

with A and B working together I'm confused on how to setup the equation

(x+y=6)+4z=1
(x+y=2)+8z=1
3x +1y + 2z =1
I don't understand how you have one equation inside another?? Try doing like they show here (like they showed you back in regular algebra).

hours to complete job alone:
A: a hours
B: b hours
C: c hours
A&B: d hours

done per hour:
A: 1/a of the job
B: 1/b of the job
C: 1/c of the job
A & B: 1/d of the job

job done:
i) 6(1/d) + 4(1/c) = 1
ii) 2(1/d) + 8(1/c) = 1
iii) 3(1/a) + 1(1/b) +2(??) = 1

Note that:

d(1/a + 1/b) = 1
d((b+a)/ab = 1
d = ab/(b+a)

But I can't get any further because your statement of relationship (iii) doesn't make sense. Who is "Z", and who is he working with "together"? Also, "x" is standing for "A", "y" is standing for "B", and "z" is standing for "Z", but what letter are you using for "C"?

Please write back with clarification. Thanks.