One job can be finished by 30 workers for 60 days. The work was started by 20 workers, and after 10 days came 5 workers. For how long will the whole work be done?
2 Answers
This is not an efficient way of solving it but demonstrates what is actually going on. My other solution is more efficient.
Explanation:
Assumption: all workers have the same rate of work per day.
Let me introduce you to a concept that may be new to you.
Effort verses time = total work done.
Let the amount of work effort be
Let the generic time in days be
Set time for 10 days as
Set unknown time as
Let the total amount of effort for the job be
Let the unknown element of time be
The actual value of
Given that the count of workers is 30 and that the time they worked was 60 days giving:
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From
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Known that total time spent working as a team was:
20 workers worked for 10 days on their own
They we joined by 5 workers so the effort they contributed was
But the initial 20 workers worked alongside the additional 5 for the same time of
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We know that
We know that
Substitute these values into
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By special request: By 'proportional' method
64 + 10 =74 days
Explanation:
You have probably come across this before
Where
Consider the inversely proportions
From this we have
Set
Then for the units we have:
workerdays is a sort of index number that just sets the relationship between the variables
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Let the unknown count of days be
Total amount of effort
Worker days would be an equivalent measure of effort. A sort of index value.
Note that the initial count of workers (20) worked for 10 days + the time (
So total time is
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