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08 Oct 2005, 14:01
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Larry can wash a car in 1 hour, Moe can wash a car in 2 hours, and Curly can wash a car in 4 hours. How long will it take them to wash a car together?
If I use the shortcut, I'll get 1x2x4/(1+2+4) = 8/7
which is incorrect...
If I use the traditional method, I'll get 1+1/2+1/4=7/4
Then RT=W
7/4t=1
t=4/7
Can someone please tell me whether the Work Formula short-cut xy/(x+y) only works for a combined rate problem of 2 people
?
I tried to apply the shortcut to the above question. But it didn't work out.
Thanks.
If I use the shortcut, I'll get 1x2x4/(1+2+4) = 8/7
which is incorrect...
If I use the traditional method, I'll get 1+1/2+1/4=7/4
Then RT=W
7/4t=1
t=4/7
Can someone please tell me whether the Work Formula short-cut xy/(x+y) only works for a combined rate problem of 2 people
?
I tried to apply the shortcut to the above question. But it didn't work out.
Thanks.
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08 Oct 2005, 14:19
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Yup.. thats only for 2 people/machines.
Rather than remembering the formulat as xy/(x+y) ... remember it as
1/x + 1/y = 1/T x, y individual times and T - when together..
So for three people/machines etc.. 1/x + 1/y + 1/z = 1/T
So for the problem, it will be 1/Larry + 1/Moe + 1/Curly = 1/together
1/1 + 1/2 + 1/4 = 1/T
or (4+2+1)/4 = 1/T or T = 7/4
Rather than remembering the formulat as xy/(x+y) ... remember it as
1/x + 1/y = 1/T x, y individual times and T - when together..
So for three people/machines etc.. 1/x + 1/y + 1/z = 1/T
So for the problem, it will be 1/Larry + 1/Moe + 1/Curly = 1/together
1/1 + 1/2 + 1/4 = 1/T
or (4+2+1)/4 = 1/T or T = 7/4
08 Oct 2005, 15:09
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omomo,
Consider 2 people, one can do the work in x hrs and the other in y hrs. in 1 hour, together, they can do -
(1/x) + (1/y) = (x+y)/xy of work => together they can do the total work in xy/(x+y) hours. This is no short-cut. It's straight 2 steps.
One we understand the work/time concept, all problems are straight forward and wouldn't take more than few steps and can be done fast. I am afraid short-cuts may not help here.
Consider 2 people, one can do the work in x hrs and the other in y hrs. in 1 hour, together, they can do -
(1/x) + (1/y) = (x+y)/xy of work => together they can do the total work in xy/(x+y) hours. This is no short-cut. It's straight 2 steps.
One we understand the work/time concept, all problems are straight forward and wouldn't take more than few steps and can be done fast. I am afraid short-cuts may not help here.
