|
Question 136148: Andrei Toom's word problem from his article http://www.inform.umd.edu/CMLT/cmltgrad/JSchaub/ta_main/toom.html
Suppose that it takes Tom and Dick 2 hours to do a certain job, it takes Tom
and Harry 3 hours to do the same job and it takes Dick and Harry 4 hours to do the same job.
How long would it take Tom, Dick and Harry to do the same job if all 3 men worked together?
is a clear rate of work problem with 3 workers.
http://www.math.umd.edu/~jnd/Algebraic_word_problems.pdf and is set up here.
I can set it up, but I can't solve it. I'd love to see it solved.
Can someone please finish it:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! let x="time together", T="Tom time alone", D="Dick time alone" , and H="Harry time alone"
"Tom and Dick 2 hours to do a certain job" __ 2/T+2/D=1
__ 3/T+3/D=1.5 __ 3/T=1.5-3/D
"it takes Tom and Harry 3 hours to do the same job" __ 3/T+3/H=1
__ substituting __ 1.5-3/D+3/H=1 __ 3/H=3/D-.5
"it takes Dick and Harry 4 hours to do the same job" __ 4/D+4/H=1
__ 3/D+3/H=.75 __ substituting __ 3/D+3/D-.5=.75 __ 6/D=5/4 __ 24=5D __ 24/5=D
substituting __ 2/T+2/(24/5)=1 __ 2/T+10/24=1 __ 2/T=14/24 __ 48=14T __ 24/7=T
substituting __ 4/(24/5)+4/H=1 __ 4/H=4/24 __ 24=H
7x/24+5x/24+x/24=1 __ 13x/24=1 __ x=24/13
|
|
|
| |
