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Two workers A and B are engaged to do a work. A working alone takes 8

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Two workers A and B are engaged to do a work. A working alone takes 8 [#permalink]

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Question Stats:

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Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need 4.5 hours more to complete the job than they both working together. What time would they take to do the work together ?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours
E. 8 hours
[Reveal] Spoiler: OA

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Re: Two workers A and B are engaged to do a work. A working alone takes 8 [#permalink]

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New post 11 Mar 2017, 02:22
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Chemerical71 wrote:
Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need
4.5 hours more to complete the job than they both working together. What time would they take to do the work together ?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours
E. 8 hours


Let A works at the rate of 'a' units/hr and B works at the rate of 'b' units/hr. A and B complete the job in x hrs.

A working alone takes 8 hours more to complete the job than if both worked together.
=> a(x+8) = (a+b)x
=> ax + 8a = ax + bx
=> 8a = bx or a = bx/8 ---(1)
If B worked alone, he would need 4.5 hours more to complete the job than they both working together

=> b(x+4.5) = (a+b)x
=> bx +4.5b = ax + bx
=> 4.5b = ax or a = 4.5b/x ---(2)

From (1) and (2), we have
\(\frac{bx}{8} = {4.5b}{x} \Rightarrow x^{2} = 4.5*8 \Rightarrow x = 6\)

Answer: (C) 6 hours.

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Re: Two workers A and B are engaged to do a work. A working alone takes 8 [#permalink]

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New post 11 Mar 2017, 03:44
ganand wrote:
Chemerical71 wrote:
Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need
4.5 hours more to complete the job than they both working together. What time would they take to do the work together ?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours
E. 8 hours


Let A works at the rate of 'a' units/hr and B works at the rate of 'b' units/hr. A and B complete the job in x hrs.

A working alone takes 8 hours more to complete the job than if both worked together.
=> a(x+8) = (a+b)x
=> ax + 8a = ax + bx
=> 8a = bx or a = bx/8 ---(1)
If B worked alone, he would need 4.5 hours more to complete the job than they both working together

=> b(x+4.5) = (a+b)x
=> bx +4.5b = ax + bx
=> 4.5b = ax or a = 4.5b/x ---(2)

From (1) and (2), we have
\(\frac{bx}{8} = {4.5b}{x} \Rightarrow x^{2} = 4.5*8 \Rightarrow x = 6\)

Answer: (C) 6 hours.
Thank you very much . :-D

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Re: Two workers A and B are engaged to do a work. A working alone takes 8 [#permalink]

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New post 11 Mar 2017, 20:58
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I did it this way and got the same result

1/x+8 + 1/x+4.5 = 1/x
1/x+4.5 = 1/x - 1/x+8
1/x+4.5 = x+8-x/(x(x+8)
1/x+4.5 = 8/(x(x+8)
x(x+8) = 8(x+4.5)
x² + 8x = 8(x+4.5)
x² = 40
x is equal to approximately 6.

Answer C

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Re: Two workers A and B are engaged to do a work. A working alone takes 8 [#permalink]

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New post 12 Mar 2017, 03:15
matthewsmith_89 wrote:
I did it this way and got the same result

1/x+8 + 1/x+4.5 = 1/x
1/x+4.5 = 1/x - 1/x+8
1/x+4.5 = x+8-x/(x(x+8)
1/x+4.5 = 8/(x(x+8)
x(x+8) = 8(x+4.5)
x² + 8x = 8(x+4.5)
x² = 40
x is equal to approximately 6.

Answer C


Hi,
This is perfectly fine. There is a typo in your solution.

x² = 40 It should be
\(x^{2}\)= 8*4.5 = 36 => x = 6

Thanks.

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Re: Two workers A and B are engaged to do a work. A working alone takes 8 [#permalink]

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New post 12 Mar 2017, 05:29
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ganand wrote:
matthewsmith_89 wrote:
I did it this way and got the same result

1/x+8 + 1/x+4.5 = 1/x
1/x+4.5 = 1/x - 1/x+8
1/x+4.5 = x+8-x/(x(x+8)
1/x+4.5 = 8/(x(x+8)
x(x+8) = 8(x+4.5)
x² + 8x = 8(x+4.5)
x² = 40
x is equal to approximately 6.

Answer C


Hi,
This is perfectly fine. There is a typo in your solution.

x² = 40 It should be
\(x^{2}\)= 8*4.5 = 36 => x = 6

Thanks.
Thank you very much for solving.

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Re: Two workers A and B are engaged to do a work. A working alone takes 8 [#permalink]

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New post 07 Jul 2017, 16:23
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Let a be the number of hours A completes work and b be the number of hours B completes work. Then (1/a) is A's rate per hour and (1/b) be B's rate per hour.
Then the rate if A and B work together is (1/a)+(1/b)=(a+b)/(ab). Time that A and B complete work is 1/[(a+b)/(ab)] = (ab)/(a+b) (this is what we want to find out)

As A works alone takes 8 hours more than A and B work together, then: a - (ab)/(a+b) = (a^2)/(a+b) = 8 (*)
As B works alone takes 4.5 hours more than A and B work together, then: b - (ab)/(a+b) = (b^2)/(a+b) = 4.5 (**)

From (*) (**), we have [(a^2)/(a+b)]*[(b^2)/(a+b)] = [(ab)^2]/[(a+b)^2] = 8*4.5 = 8*9/2 = 36
then (ab)/(a+b) = sqrt (36) = 6 => Answer

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Re: Two workers A and B are engaged to do a work. A working alone takes 8 [#permalink]

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New post 07 Jul 2017, 18:04
Chemerical71 wrote:
Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need
4.5 hours more to complete the job than they both working together. What time would they take to do the work together ?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours
E. 8 hours


Plugging numbers is less time consuming than the algebraic method for me. Let's start with C since it's the middle value.

\(\frac{1}{6+8} + \frac{2}{12+9} =? \frac{1}{6}\)

\(\frac{2}{28} + \frac{2}{21} =? \frac{1}{6}\)

\(\frac{2}{7}(\frac{1}{4} + \frac{1}{3}) =? \frac{1}{6}\)

\(\frac{2}{7} * \frac{7}{12} =? \frac{1}{6}\)

\(\frac{2}{12} = \frac{1}{6}.\) So, this is the answer. Ans - C.
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Re: Two workers A and B are engaged to do a work. A working alone takes 8 [#permalink]

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New post 28 Aug 2017, 14:00
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1/(t+8) + 1/(t+4.5) = 1/t
t(2t + 12.5) = (t +8)(t+4.5)
t^2 = 36
t = 6

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Re: Two workers A and B are engaged to do a work. A working alone takes 8 [#permalink]

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New post 28 Aug 2017, 19:17
Hi,

The general framework of the above problem:

Total time taken to complete the work (working together) = \(x\) hrs

Time taken by A to complete the work (working alone) = \(a\) hrs more than combined time, i.e. \((x+a)\) hrs

Time taken by B to complete the work (working alone) = \(b\) hrs more than combined time, i.e. \((x+b)\) hrs

Then \(x = \sqrt{a \times b}\)

In the above problem \(a = 8\) hrs, and \(b = 4.5\) hrs. Hence \(x = \sqrt{a \times b} = \sqrt{8 \times 4.5} = \sqrt{36} = 6\) hrs.

Thanks.

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Re: Two workers A and B are engaged to do a work. A working alone takes 8   [#permalink] 28 Aug 2017, 19:17
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