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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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10 Mar 2017, 22:30

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68% (02:05) correct
32% (03:17) wrong based on 99 sessions

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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

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

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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 \(\frac{bx}{8} = {4.5b}{x} \Rightarrow x^{2} = 4.5*8 \Rightarrow x = 6\)

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

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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 \(\frac{bx}{8} = {4.5b}{x} \Rightarrow x^{2} = 4.5*8 \Rightarrow x = 6\)

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

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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

-- Please give a kudos if you find this post useful.

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

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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.

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