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Question 148609: Suppose it takes Tom and Dick 2 hours to do a certain job, it takes Tom and Harry 3 hours to do the same job. It takes Dick and Harry 4 hours to do this same job.
How long will it take Tom, Dick, and Harry to do the same job together?
So, just for organizing:
T + D = 2hrs
T + H = 3hrs
D + H = 4hrs
T+D+H = ? hrs
Therefore: (I think, but I'm sure it's most probably right)
1/T + 1/D =1/2
1/T + 1/H =1/3
1/D + 1/H =1/4
1/T + 1/D + 1/H =1/x
So far, I got to T=12/5 and D=12
using reciprocals and the first equation, the sum is 6/12 or 1/2; so far so good.
But I've tried using it to solve for the H one.. and it doesn't quite work.. so when I get to the last equation I still have two variables, H and X.
^
I posted this before, and my teacher said the answer was wrong. I used ptaylor's solution and method rather than Stan H's solution. seeing as we're looking for hours. anyway, I inverted 24/13 to 13/24 which is approx half an hour vs almost two hours. I'm sure that's the right solution since my teacher said 1 hr and 51 mins is too long.
Any comments?
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! 1/T + 1/D =1/2
1/T + 1/H =1/3
1/D + 1/H =1/4
1/T + 1/D + 1/H =1/x __ all this is correct
from 3rd eqn __ 1/H=1/4-1/D
substituting into 2nd eqn __ 1/T+1/4-1/D=1/3 __ adding 1st eqn __ 2/T+1/4=5/6 __ subtracting 1/4 __ 2/T=7/12
__ "cross" multiplying __ 24=7T __ dividing by 7 __ 24/7=T
substituting __ 7/24+1/D=1/2 __ subtracting 7/24 __ 1/D=5/24 __ inverting __ D=24/5
substituting __ 7/24+1/H=1/3 __ subtracting 7/24 __ 1/H=1/24 __ inverting __ H=24
7/24+5/24+1/24=1/x __ 13/24=1/x __ inverting __ 24/13=x
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