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Work Problem: 3 machines R, S, and T, working together at ..

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Work Problem: 3 machines R, S, and T, working together at ..

by II » Thu Jul 10, 2008 2:16 pm
3 machines R, S, and T, working together at their respective rates, can do a certain job in 4 hours.
S and T, working together at their respective rates, can do the same job in 5 hours. How many hours would it take R, working alone at its rate, to do the same job ?

A) 8
B) 10
C) 12
D) 15
E) 20

This is a straightforward question ... I would say a 500-550 level question ... I am just keen to find out the following for this:
- trap/trick answers in the answer choices ... what are they and how can you spot them ?
- guessing strategy ... if you had to guess on this question, how would you guess ? which answer choices would you cross out ?
- alternative approaches ?
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Re: Work Problem: 3 machines R, S, and T, working together a

by olika » Thu Jul 10, 2008 2:27 pm
We have
1/r+1/t+1/s=1/4 and 1/t+1s=1/5

Therefore
1/r+1/5=1/4, 1/r=1/20, r=20.
The answer is 20 hours.
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by II » Thu Jul 10, 2008 3:05 pm
yes Olika ... you are right. As mentioned this is an easy question.

I am more interested in learning about:
- trap/trick answers in the answer choices ... what are they and how can you spot them ?
- guessing strategy ... if you had to guess on this question, how would you guess ? which answer choices would you cross out ?
- alternative approaches ?
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by lion147 » Thu Jul 10, 2008 6:21 pm
II wrote:yes Olika ... you are right. As mentioned this is an easy question.

I am more interested in learning about:
- trap/trick answers in the answer choices ... what are they and how can you spot them ?
- guessing strategy ... if you had to guess on this question, how would you guess ? which answer choices would you cross out ?
- alternative approaches ?
I saw your method involving pizzas (!) earlier, and worked this out in my head in about 15 seconds, which would save me a load of time on the test.

Thanks!

For those that didn't see the pizza method:

R+S+T can make 100 pizzas in 4 hours.
S+T can make 100 pizzas in 5 hours.
S+T make 20 pizzas per hour together.

In 4 hours, S+T make 4*20=80 pizzas.
Which means R makes the remaining 20 pizzas in 4 hours.
R makes 5 pizzas per hour.
100 pizzas would take R 100/5=20 hours on its own.
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