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Math Expert V
Joined: 02 Sep 2009
Posts: 62531
Two workers A and B are engaged to do a work. A working alone takes 8  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 71% (02:44) correct 29% (02:49) wrong based on 72 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

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Director  D
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Posts: 555
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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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Bunuel 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

Are You Up For the Challenge: 700 Level Questions

$$(A+B)t=1$$ or $$(A+B)=\frac{1}{t}$$
$$A(t+8)=1$$ or $$A=\frac{1}{t+8}$$
$$B(t+4.5)=1$$ or $$B=\frac{1}{t+4.5}$$

$$\frac{1}{t+8}+\frac{1}{t+4.5}=\frac{1}{t}$$

$$\frac{1}{t+4.5}=\frac{1}{t}-\frac{1}{t+8}$$

$$\frac{1}{t+4.5}=\frac{t+8-t}{t(t+8)}$$

$$t(t+8)=8(t+4.5)$$

$$t^2+8t=8t+36$$

$$t^2=36$$

$$t=6$$

GMAT Tutor B
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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:
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?

Solution:
Let A and B together take t hours to complete the work.
Thus, time taken by A = (t + 8) hrs and time taken by B = (t + 4.5) hrs

Thus, we can say that:
Work done by (A and B) in t hours = Work done by A in (t + 8) hours = Total work
=> (Work done by A in t hrs) + (Work done by B in t hrs) = (Work done by A in t hrs) + (Work done by A in 8 hrs)

Cancelling the (Work done by A in t hrs) from both sides:
(Work done by B in t hrs) = (Work done by A in 8 hrs)
=> Work done by B in 1 hr = Work done by A in (8/t) hrs ... (i)

Similarly, we have:
Work done by (A and B) in t hours = Work done by B in (t + 4.5) hours = Total work
=> (Work done by A in t hrs) + (Work done by B in t hrs) = (Work done by B in t hrs) + (Work done by B in 4.5 hrs)

Cancelling the (Work done by B in t hrs) from both sides:
(Work done by A in t hrs) = (Work done by B in 4.5 hrs)
=> Work done by B in 1 hr = Work done by A in (t/4.5) hrs ... (ii)

Thus, from (i) and(ii):
8/t = t/4.5

=> $$t^2 = 36$$
=> t = 6 hrs

Alternate approach
Let time taken by A and B together be t hours
Thus, time taken by A = (t + 8) hrs and time taken by B = (t + 4.5) hrs

thus, equating work done by A and B in 1 hour:
1/(t + 8) + 1/(t + 4.5) = 1/t

Solving, we get: t = 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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1
Bunuel 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

Are You Up For the Challenge: 700 Level Questions

A short little formula exists which can solve it in 10 secs -

$$\sqrt{8*4.5}$$

$$= \sqrt{36}$$

$$= 6$$ , Answer must be (C)
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Abhishek....

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Joined: 24 Nov 2016
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Location: United States
Re: Two workers A and B are engaged to do a work. A working alone takes 8  [#permalink]

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Bunuel 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

r=w/t

(a+b)=1/t
a=1/t+8
b=1/t+4.5
(1/t+8)+(1/t+4.5)=1/t
2t^2+12.5t=t^2+12.5t+36
t^2=36 (t>0) t=6

Ans (C)
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Posts: 1272
Location: United States (KS)
GMAT 1: 600 Q46 V27 Re: Two workers A and B are engaged to do a work. A working alone takes 8  [#permalink]

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Quote:

A short little formula exists which can solve it in 10 secs -

$$\sqrt{8*4.5}$$

$$= \sqrt{36}$$

$$= 6$$ , Answer must be (C)

Abhishek009

Any theory or links on how this is achievable and in what conditions it usually works?

Thank you!
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Target Test Prep Representative V
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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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1
Bunuel 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

Are You Up For the Challenge: 700 Level Questions

Let’s let n = the number of hours it takes to complete the job when A and B work together; thus, their combined rate is 1/n. Since A alone takes 8 hours more than if they work together, then A’s rate is 1/(n + 8). And since B alone takes 4.5 hours more than if they work together, then B’s rate is 1/(n + 4.5).

Thus, , we can create the rate equation:

1/(n + 8) + 1/(n + 4.5) = 1/n

Multiplying by n(n + 8)(n + 4.5), we have:

n(n + 4.5) + n(n + 8) = (n + 8)(n + 4.5)

n^2 + 4.5n + n^2 + 8n = n^2 + 4.5n + 8n + 36

2n^2 + 12.5n = n^2 + 12.5n + 36

n^2 = 36

n = 6 or -6

Since n can’t be negative, n = 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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TheNightKing wrote:
Quote:

A short little formula exists which can solve it in 10 secs -

$$\sqrt{8*4.5}$$

$$= \sqrt{36}$$

$$= 6$$ , Answer must be (C)

Abhishek009

Any theory or links on how this is achievable and in what conditions it usually works?

Thank you!

RESPONDING TO A PM IN THIS REGARD -

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

Time required to complete the task will be $$\sqrt{ab}$$

It can be applied to all such cases without any restriction !!
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Re: Two workers A and B are engaged to do a work. A working alone takes 8   [#permalink] 20 Feb 2020, 07:21
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