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If x men can do a job in h days, how long would y men take to do the

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If x men can do a job in h days, how long would y men take to do the  [#permalink]

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New post 26 Feb 2018, 22:25
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

53% (01:06) correct 47% (01:11) wrong based on 62 sessions

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If x men can do a job in h days, how long would y men take to do the  [#permalink]

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New post 26 Feb 2018, 22:48
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Bunuel wrote:
If x men can do a job in h days, how long would y men take to do the same job?

A. x/h
B. xh/y
C. hy/x
D. xy/h
E. x/y


If x men do a job in h days, 1 man will do the work in \(hx\) days*

Therefore, y men will have \(\frac{hx}{y}\) days to do the same job (Option B)

*If x=5 men do a work in 20 days(assuming a man does 1 unit a day) they would a total of 100 units.
If 1 man must finish the work on his own(rate - 1 unit/day), he takes 100 days to finish the 100 units.
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If x men can do a job in h days, how long would y men take to do the  [#permalink]

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New post 27 Feb 2018, 18:30
Bunuel wrote:
If x men can do a job in h days, how long would y men take to do the same job?

A. x/h
B. xh/y
C. hy/x
D. xy/h
E. x/y

Algebra
The standard work formula is (R * T) = W

When problems include "number of workers" (or machines), you can modify the standard formula.

Then manipulate it just as you would RT=W, to find what you need.

Add one more variable to LHS, thus:
(# of men\(* R * T) = W\)

Values given:
# = \(x\)
T = \(h\) (days)
W = 1 (job)

Find the rate of one man.
(# of men) * R * T = W

\(R = \frac{W}{(Number*T)}\)

\(Rate =\frac{1}{x*h}=\frac{1}{xh}\)

At that rate, how long will it take \(y\) to do the same job?
# of men = \(y\)
Rate = \(\frac{1}{xh}\)
Time = ??
Work = 1 (job)

(# of men) * R * T = W
\(T=\frac{W}{(Number*Rate)}\)

\(T=\frac{1}{(y*\frac{1}{xh})}=\frac{1}{(\frac{y}{xh})}=1*\frac{xh}{y}=\frac{xh}{y}\)


Answer B

Assign values
To avoid more than one correct answer:
-- don't use 1 in rate problems, and
-- include one slightly larger number

(# of men) * Rate * Time = Work
Let x (# of men) = 2
Let h (# of days) = 3
Let y (new # of men) = 8
Work = 1 job

Rate of one man?
(#) * R * T = W
(2) * (R) * (3) = 1
Rate = \(\frac{1}{(2*3)}\)
Rate of one man = \(\frac{1}{6}\)

At that rate, time it will take y=8 men to do the same job?
(Number of men) * R * T = W

T = \(\frac{W}{(Number*Rate)}\)

Time = \(\frac{1}{(8*\frac{1}{6})}=\frac{1}{(\frac{8}{6})}=1*\frac{6}{8}=\frac{3}{4}\)

With x=2, h=3, and y=8, find the answer that yields \(\frac{3}{4}\) (days)

A. x/h: \(\frac{2}{3}\). NO

B. xh/y: \((\frac{2*3}{8})=\frac{6}{8}=\frac{3}{4}\) MATCH

C. hy/x: \((\frac{3*8}{2})=\frac{24}{2}=12\). NO

D. xy/h: \((\frac{2*8}{3})=\frac{16}{3}\). NO

E. x/y: \((\frac{2}{8})=\frac{1}{4}\). NO

Answer B

P.S. A modified RT=W chart, with (# of workers) added to LHS, usually makes these problems easier.
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Re: If x men can do a job in h days, how long would y men take to do the  [#permalink]

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New post 27 Feb 2018, 22:06
Bunuel wrote:
If x men can do a job in h days, how long would y men take to do the same job?

A. x/h
B. xh/y
C. hy/x
D. xy/h
E. x/y

IMO B total work will be X*h and to find number of days we need to divide it by y
so answer is xh/y
It will be easy to understand by plugging value in question:-
X=10 h=1 and y=3
total work is 10 and number of hours that 3 man will complete is 10/3= 3.33
if you will plot above assumed values in question only B will give u answer as 3.333
If you like my explanation then please prove me KUDOS
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Re: If x men can do a job in h days, how long would y men take to do the &nbs [#permalink] 27 Feb 2018, 22:06
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