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Question 1038207: Paul can do a certain job in half the time that Jim requires to do it. Jim worked alone for an hour and stopped; then Paul completed the job in 10 hours. What length of time, in hours, would Paul, working alone, take to do the whole job?
Found 6 solutions by mananth, MathTherapy, ikleyn, n2, josgarithmetic, KMST:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! Paul can do a certain job in half the time that Jim requires to do it.
Jim worked alone for an hour and stopped; then Paul completed the job in 10 hours. What length of time, in hours, would Paul, working alone, take to do the whole job?
Let jim take x hours to do the job
So he does 1/x of the job in 1 hour
Paul takes x/2 hours to do the job
so he does 2/x of the job in 1 hour
After jim worked for 1 hour balance job was
(1-1/x) = (x-1)/x
Paul does 2/x of the job in 1 hour
so he takes ((x-1)/x)/(2/x) hours to do the remaing job
((x-1)/x)/(2/x) = 10
(x-1)/x =5x
x-1=5
x= 4 No of hours Jim takes to complete the job
Paul will take 2 hours
Answer by MathTherapy(10719)  (Show Source):
You can put this solution on YOUR website!
Paul can do a certain job in half the time that Jim requires to do it. Jim worked alone for an hour and stopped; then Paul completed the job in 10 hours. What length of time, in hours, would Paul, working alone, take to do the whole job?
Working alone, Paul takes:  to do the job
Answer by ikleyn(53619)  (Show Source):
You can put this solution on YOUR website! .
Paul can do a certain job in half the time that Jim requires to do it.
Jim worked alone for an hour and stopped; then Paul completed the job in 10 hours.
What length of time, in hours, would Paul, working alone, take to do the whole job?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The solution by @mananth to this problem is INCORRECT.
It is obvious if to compare his answer with the given data in the problem.
I came to bring a correct solution.
Let 'a' be the Jim's rate of work, i.e. part of work, which Jim makes in 1 hour.
Then the Paul's rate of work is 2a, according to the problem.
Jim worked alone for an hour and stopped; then Paul completed the job in 10 hours.
It means that
a + 10*(2a) = 1, where '1' represents the whole job.
From this equation, we find
a + 20a = 1 ---> 21a = 1 ---> a = 1/21.
It means that Jim makes 1/21 of the Job per hour.
In other words, Jim needs 21 hours to make the whole job alone.
Hence, according to the problem, Paul needs half of 21 hours to make the whole job alone.
In other words, Paul needs 21/2 = 10.5 hours to make the whole job alone. ANSWER
At this point, the problem is solved completely and correctly.
-------------------------
What we observe in this case, is very typical situation.
The solution by @mananth was created by a computer code - which was a prototype of an Artificial Intelligence in its current state.
As soon as this code met a non-standard formulation, it produced wrong solution (= kind of gibberish).
Not only it produced wrong solution - it even did not check it, even did not notice it and even did not react
on wrong solution.
It shows, that the AI is in its infantile state and can work properly only if real persons and experts
accompany its work, checking every step.
Answer by n2(54)  (Show Source):
You can put this solution on YOUR website! .
Paul can do a certain job in half the time that Jim requires to do it.
Jim worked alone for an hour and stopped; then Paul completed the job in 10 hours.
What length of time, in hours, would Paul, working alone, take to do the whole job?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let 'a' be the Jim's rate of work, i.e. part of work, which Jim makes in 1 hour.
Then the Paul's rate of work is 2a, according to the problem.
Jim worked alone for an hour and stopped; then Paul completed the job in 10 hours.
It means that
a + 10*(2a) = 1, where '1' represents the whole job.
From this equation, we find
a + 20a = 1 ---> 21a = 1 ---> a = 1/21.
It means that Jim makes 1/21 of the Job per hour.
In other words, Jim needs 21 hours to make the whole job alone.
Hence, according to the problem, Paul needs half of 21 hours to make the whole job alone.
In other words, Paul needs 21/2 = 10.5 hours to make the whole job alone. ANSWER
Answer by josgarithmetic(39736) (Show Source):
Answer by KMST(5337)  (Show Source):
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