SOLUTION: Jack can build a wall on his own in 16 hours. Jill can build the same wall in 12 hours working alone.. If they work together they can build the wall in 8 hours, but because theyso

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jack can build a wall on his own in 16 hours. Jill can build the same wall in 12 hours working alone.. If they work together they can build the wall in 8 hours, but because theyso      Log On


   

Question 761804: Jack can build a wall on his own in 16 hours. Jill can build the same wall in 12 hours working alone.. If they work together they can build the wall in 8 hours, but because theysometimes get in each others way, they lay 16 bricks less per hour between them than if they didn’t get in each other’s way. So the question is… How many bricks are there in the wall?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Let b = the interference rate when Jack and Jill build together.
Without interferences, you expect the combined rate to be 1/16+1/12,
but in the situation, the actual rate is combined with b jobs per hour in the opposite direction:

1%2F16%2B1%2F12=b%2B1%2F8 where b%3C0.
LCD is 2*2*2*2*3, so simplifying and here omitting the steps,
(Multiplying both sides first by the LCD)
48%2Ab=3%2B4-6
highlight%28b=1%2F48%29 jobs per hour but IN THE OPPOSITE DIRECTION.

That is 1 job per 48 hours as an interference. This is the same ratio as the 16 bricks per hour.

We have a proportion.
{16 bricks / 1 hour} = { 1 job / 48 hours }.
We want to increase BOTH numerator and denominator on the left so that we match the 48 hour value. We do it like this:

%2816%2F1%29%2A%2848%2F48%29 to obtain the same denominator of 48 hours.
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RESULT: 768 bricks are in the whole job, one wall.
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