SOLUTION: a mason can build a wall in 6 hours less than an apprentive. together they can build the wall in 4 hours. how long would it take the apprentice, working alone, to build the wall?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a mason can build a wall in 6 hours less than an apprentive. together they can build the wall in 4 hours. how long would it take the apprentice, working alone, to build the wall?      Log On


   

Question 347067: a mason can build a wall in 6 hours less than an apprentive. together they can build the wall in 4 hours. how long would it take the apprentice, working alone, to build the wall?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes the apprentice working alone to build the wall
Then the apprentice works at the rate of 1/x wall per hour
And x-6=amount of time it takes the mason to build the wall
Then the mason works at the rate of 1/(x-6) wall per hour
Together the mason and apprentice works at the rate of 1/4 wall per hour
So our equation to solve is:
1/x + 1/(x-6)=1/4 multiply each term by 4x(x-6)
4(x-6)+4x=x(x-6) get rid of parens
4x-24+4x=x^2-6x or
8x-24=x^2-6x subtract 8x from and add 24 to both sides
x^2-6x-8x+24=0
x^2-14x+24=0 ----quadratic in standard form and it can be factored
(x-2)(x-12)=0
x=2 hrs----THIS CANNOT BE A SOLUTION; THE MASON CANNOT WORK 6 HRS LESS THAN 2 HOURS ---CANNOT HAVE NEGATIVE TIMES IN THIS CASE
x=12 hrs----time it takes apprentice working alone
Then mason takes 6 hrs working alone to build the wall
CK
1/12 + 1/6=1/4
3/12=1/4
1/4=1/4
Hope this helps---ptaylor