# math problem..driving me crazy!!!

Discussion in 'DAT Discussions' started by smile101, May 15, 2008.

1. ### smile101

Joined:
Dec 4, 2007
Messages:
401
0
Status:
Pre-Dental
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?
A. 1 2/3 mon
B. 1 7/8 mon
C. 2 1/6 mon
D. 2 1/5 mon
E. 3 1/3 mon

3. ### joh020340

Oh boy I am not sure at all about what I'm about to say but I'm going to try it anyways, and people can comment. So 25 workers can do a job in 5 months, so 1 worker does 1/5 of the job. Now use that rate (1/5) to fine out the total. (25)(1/5) + (15)(1/5)(5/6) = 7.5. I'm flyin by the seat of my pants so I'm not sure what that is. so rate x time = job? so 7.5x=5, x=3.33. so 5-3.33 is 1.66 which is A. Again like I said I have no idea what I did or what my intermediate numbers stand for.

4. ### Streetwolf Ultra Senior Member Dentist

Joined:
Oct 25, 2006
Messages:
1,801
5
Status:
Dentist
The full time staff of 25 finishes a job in 5 months. Each temp worker is 5/6 as efficient as the full time worker, and 15 of them are hired. If each temp worker is 5/6 as efficient, then this means you have the equivalent of 15(5/6) = 12.5 full time workers. So in reality you have 37.5 full time workers which is 1.5x (3/2) the original amount. That means the job can be finished in 2/3 the time which would be (2/3)5 = 3 and 1/3 months. So you save 1 and 2/3 months which is choice (A).

5. ### smile101

Joined:
Dec 4, 2007
Messages:
401
0
Status:
Pre-Dental
thanks guys!!!

6. ### joh020340

Much better way than mine. Plus, you seemed to know the process while doing it, better than just a hunch.

7. ### dentalplan

Joined:
Mar 1, 2008
Messages:
140
0
Status:
Pre-Dental
Streetwolf: I like your reasoning, but can you explain something to me?

What exactly is the logical connection between "So in reality you have 37.5 full time workers which is 1.5x (3/2) the original amount."

and......

"That means the job can be finished in 2/3 the time"

For some reason I can't grasp my head around this one....Can you explain, or show logically, exactly how you can assume that 1.5 that amount of full time workers means the job can be done in 2/3 the time?

I hope you can explain it with more depth than just 3/2 is the reciprocal of 2/3, which is the fraction of time the job will be done.

I want to know the exact logic behind that ^^

I just can't make the connection.

I tried making myself equations...but they just ended up looking like: 25/time= rate. So 25/5 months = rate of 5 men per month. And then dividing 37.5 by that rate (5) to get the new time. Yeah.....it doesn't really make sense. I hope you can clear it up a bit.

8. ### doc3232

Joined:
Feb 15, 2008
Messages:
3,809
9
Status:
Dental Student

Ok, 3/2 and 2/3 are not the best numbers to visualize, why not change it?

How about double, so 10 workers finish in 5 mins, what if you doubled the workers.
if you double the speed then you must half the time, hence 2.5 mins.
Same concept with 3/2 and 2/3.
Never bother with equations, they WILL confuse the best of us.
Hope that clears it up.

9. ### sl2obel2ts i like tomatoes

Joined:
Sep 26, 2007
Messages:
602
4
Status:
Dentist
or...
25 * 5 = 125
125 = (25+5/6*15)*X
solve for X
X = 10/3
Answer: 5 - 10/3 = 5/3

10. ### Streetwolf Ultra Senior Member Dentist

Joined:
Oct 25, 2006
Messages:
1,801
5
Status:
Dentist
n people * t months = 1 complete job.
(3/2)n people * t months = (3/2) complete job.

You want to keep the same # of people and only do 1 complete job so the only thing to do is multiply the time by (2/3).

I know this isn't a great formula but it should help you visualize what's going on a bit better.

====

Another way:

n workers do 1 complete job in 5 months, so 1 worker does (1/n) complete job in 5 months, and thus (1/5n) complete job in 1 month. Now let's say you have (3/2)n workers. In 1 month they would do (3/10) the job --> (3/2)n * (1/5n). But you want a full job done. So 1 / (3/10) = 10/3 --> this represents the # of times they need to complete (3/10) of the complete job. Thus you need 10/3 months for (3/2)n workers to finish 1 complete job.

Joined:
May 15, 2008
Messages:
228