Quantitative Reasoning Question Help

[Rook]

Hey Guys,
I was hoping someone could help me figure this out:
Question:
A construction firm receives an important contract and
hires 15 temporary workers in addition to its full-time
staff. If the entire full-time staff of 25 could complete
the job in five months, and if temporary workers work
5/6 as fast as full-time workers, how much time will
be saved by hiring the additional workers?

I am not looking for an answer but more of an explanation of how to get to the answer. Thanks so much!!

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[Lonely Sol]

Hey Guys,
I was hoping someone could help me figure this out:
Question:
A construction firm receives an important contract and
hires 15 temporary workers in addition to its full-time
staff. If the entire full-time staff of 25 could complete
the job in five months, and if temporary workers work
5/6 as fast as full-time workers, how much time will
be saved by hiring the additional workers?

I am not looking for an answer but more of an explanation of how to get to the answer. Thanks so much!!

First
You have 25 Original workers that can complete the "X" amount of work in 5 months. Now you added 15 more workers that can do "X" amount of work in 5/6 the time it takes for the original workers.

5/6(15) will the amount of temporary workers that you would have if they worked the same as original workers.

Now add the original and the new Temporary workers together:
25 + 5/6(15) = 37.5 workers

So, now you have 37.5 workers who does the same job "X" in same time (5 mths) instead of 25 workers who also took 5 months.
Now you find out how fast will the job be done if you had 37.5 workers instead of 25, So: 37.5/25 = 1.5.

1.5 basically means that Job "X" is done 1.5 as fast as the orginal in 5 months. you can put it into equation form: 1.5X = 5

Solve for X. You get X = 5/1.5, which is the same as 5*(2/3).
SImplifing it will give you 10/3. That basically means thats howmuch time it will take if there were 37.5 workers instead of 25

So, Now you minus that number from 5. You get 5-(10/3) = 5/3 or 1 2/3.


Hope this helps!!

 

[Rook]

First
You have 25 Original workers that can complete the "X" amount of work in 5 months. Now you added 15 more workers that can do "X" amount of work in 5/6 the time it takes for the original workers.

5/6(15) will the amount of temporary workers that you would have if they worked the same as original workers.

Now add the original and the new Temporary workers together:
25 + 5/6(15) = 37.5 workers

So, now you have 37.5 workers who does the same job "X" in same time (5 mths) instead of 25 workers who also took 5 months.
Now you find out how fast will the jobe be done if you had 37.5 workers instead of 5, So: 37.5/25 = 1.5.

1.5 basically means that Job "X" is done 1.5 as fast as the orginal in 5 months. you can put it into equation form: 1.5X = 5

Solve for X. You get X = 5/1.5, which is the same as 5*(2/3).
SImplifing it will give you 10/3. That basically means thats howmuch time it will take if there were 37.5 workers instead of 25

So, Now you minus that number from 5. You get 5-(10/3) = 5/3 or 1 2/3.


Hope this helps!!

Lonely Sol!!
THANK YOU SO MUCH!!! I had the hardest time visualizing this but you broke it down really well...(u should consider tutoring!!)
Take care!!
Rook

 

[Lonely Sol]

Lonely Sol!!
THANK YOU SO MUCH!!! I had the hardest time visualizing this but you broke it down really well...(u should consider tutoring!!)
Take care!!
Rook

I am glad it helped you!!