Employee Task

[Anna-Lisa]

Just had some problems with solving the following task, maybe you can give me an approach!
In 1955, 300 of a company´s 750 employees were women, In 1987, the company had 900 employees, 430 oh whom were women. The number of female employees increased by what percent from 1955 to 1987?
Thanks

[kvcpk]

Just had some problems with solving the following task, maybe you can give me an approach!
In 1955, 300 of a company´s 750 employees were women, In 1987, the company had 900 employees, 430 oh whom were women. The number of female employees increased by what percent from 1955 to 1987?
Thanks

If the question is asking Percentage increase of NUMBER of female employees, then

in 1955 - 300 women
in 1987 - 430 women

hence perc increase = (430-300)/300 * 100 = 130/3 = 43.33%

If the question is asking Percentage increase in the ratio of female employees, then
in 1955 - 300/750
in 1987 - 430/900

perc inc = (430/900 - 300/750)/300/750 *100
=(750*430 -300*900)/3*900
=(322500-270000)/3*900
=19.4%

Hope this helps!!

[ankur.agrawal]

Hey Lisa can u pls confirm the answer.

[ankur.agrawal]

300/750=40% of the employees were women. i.e per 100 employee, 40 are women. - 1955

430/900=48% of the employees were women. i.e per 100 employee, 48 are women - 1987

So if we compare per 100 employee - then the % increase in rate should be 48-40=8% approx.

Pls correct if this is absurd.

[Anna-Lisa]

Thanks 43 1/3 is the right answer. that´s what i have in my answer key, but i didn´t knew before how to get there!
Maybe you can explain the following task to me too!
If n identical pipes can fill an x-gallon pool in t hours, then at the same rate how long will it take one such pipe to fill a y-gallon pool?
Thanks for helping me

[kvcpk]

If n identical pipes can fill an x-gallon pool in t hours, then at the same rate how long will it take one such pipe to fill a y-gallon pool?
Thanks for helping me

n-pipes fill x-gallon pool in t hours.
n-pipes can fill x/t gallons in 1 hour.
1 pipe can fill x/tn gallons in hour.

Now, we need the number of hours taken to fill y-gallon pool by 1 pipe.

1 pipe can fill
x/tn gallons in 1 hour.
y gallons - how many hours??
=y/(x/tn)
=tny/x hours

what is OA?

[kmittal82]

Thanks 43 1/3 is the right answer. that´s what i have in my answer key, but i didn´t knew before how to get there!
Maybe you can explain the following task to me too!
If n identical pipes can fill an x-gallon pool in t hours, then at the same rate how long will it take one such pipe to fill a y-gallon pool?
Thanks for helping me

n idential pipes fill x gallons in t hours
1 pipe fills x/n gallons in t hours
1 pipe fills x/nt gallons in 1 hour
1 gallon is filled by 1 pipe in nt/x hours
1 pipe takes (nt/x)*y = nty/x hours to fill y gallons.

Not sure if this is the right answer though

[Anna-Lisa]

Thanks, here´s already the next question, actually pretty easy.
Brian read 108 pages of a novel on tuesday. On wednesday he read the remaining 192 pages, reading at the same average rate he read on tuesday. if his reading on wednesday took 3 hours longer than his reading on tuesday, what is his average reading rate in pages per hour!

[puneetdua]

Hi Lisa -

Is the ans to Braian's Avg speed ...is 28 ?

Thnaks

[Anna-Lisa]

Hi Lisa -

Is the ans to Braian's Avg speed ...is 28 ?

Thnaks

Yes it is! Let me know how you did it!

[tomada]

Let X= # of hours Brian needs to read 108 pages on Tuesday.

We're told that Brian needs 3 more hours to read 192 pages than he needed to read 108 pages.

Let X+3 = # of hours Brian needs to read 192 pages on Wednesday.

The rate at which Brian reads on Tuesday = 108 pages/X hours, or 108/X pages per hour
The rate at which Brian reads on Wednesday = 192 pages/(X+3) hours, or 192/(X+3) pages per hour

Since we are told that the rate at which Brian reads on Tuesday is the same as the rate at which he reads on Wednesday, we can set these two rates equal to each other:

108/X = 192/(X+3) ==> X= 27/7

Since Brian needs X hours to read on Tuesday and X+3 hours to read on Wednesday, he spends a total of X+(X+3)= 2X+3 hours to read 108+192=300 pages.

This overall rate can be expressed as 300 pages/2X+3 hours, or 300/(2x+3) pages per hour.

When you plug in 27/7 for X, the overall rate is calculated to be 28 pages per hour.

Hi Lisa -

Is the ans to Braian's Avg speed ...is 28 ?

Thnaks

Yes it is! Let me know how you did it!

[HPengineer]

I think i got tripped up on this one...

I took 2x + 3 = 300 and solved for x... Thats not the correct approach? Is there still away to solve the problem if you come in at this angle?

[tomada]

Essentially, this method is comparing apples and oranges. It's important to remember the units of measurement.
On the right-hand side of the equation, you have 300 (pages).
On the left-hand side, there's the term 2x+3 (hours).

I think i got tripped up on this one...

I took 2x + 3 = 300 and solved for x... Thats not the correct approach? Is there still away to solve the problem if you come in at this angle?

[Anna-Lisa]

Essentially, this method is comparing apples and oranges. It's important to remember the units of measurement.
On the right-hand side of the equation, you have 300 (pages).
On the left-hand side, there's the term 2x+3 (hours).

I think i got tripped up on this one...

I took 2x + 3 = 300 and solved for x... Thats not the correct approach? Is there still away to solve the problem if you come in at this angle?

Thanks for helping me i didn´t calculate the 2x+3!

[roh00kan]

Basically, 'x' - the time to read 108 pages is 27/7.

Since Brian needs additional 3 hours to read 192, the total time required for Brian to read 300 (108+192) is x+x+3 = 2x+3

Now 2x+3 is the time. We need the Avg rate. So we need to divide total pages Brian read with total time.

Avg Rate = 300/(2x+3)

Substitute for x

Rate = 300/(2*27/7 + 3) = 300*7/(54+21) = 4*7 = 28.

HPEngineer, your mistake was, you didn't consider the rate. If you are not familiar, write down the formula. R*T = Total. That helps, especially for word problems. So when you have an eq 2x+3 = 300, you are bound to make mistake.
When you write Avg R*total time = total pages read, you can avoid unnecessary mistakes.