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

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 ?

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

Are You Up For the Challenge: 700 Level Questions

Abhishek009 · Accepted Answer

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

\sqrt{8*4.5}

= \sqrt{36}

= 6  , Answer must be (C)

firas92 · Answer

(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

Answer is  (C)

sujoykrdatta · Answer

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

Answer C

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
 Answer C

exc4libur · Answer

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)

TheNightKing · Answer

Abhishek009

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

Thank you!

ScottTargetTestPrep · Answer

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.

Answer: C

Abhishek009 · Answer

RESPONDING TO A PM IN THIS REGARD -

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

It can be applied to all such cases without any restriction !!

Jihyo · Answer

let us assume the time taken to do the work together = x hours

Time taken by A to do the work alone = x+8 hours
Time taken by B to do the work alone =x+4.5 hours

L.C.M=(x+8)(x+4.5)=TOTAL WORK
Rate of A = x+4.5 part of work per hour
Rate of B= x+8 part of work per hour
Rate of A & B working together= (x+4.5+x+8)=(2x+12.5) part of work per hour

RATE*TIME TAKEN=TOTAL WORK
=>(2x+12.5)*x=(x+8)(x+4.5)
=>x^2=36
=>x=6

Answer:6 hours.

Kinshook · Answer

Given:  
1. Two workers A and B are engaged to do a work. 
2. A working alone takes 8 hours more to complete the job than if both worked together.
3. If B worked alone, he would need 4.5 hours more to complete the job than they both working together.

Asked:  What time would they take to do the work together ?

Let us assume that they take x hours working together to complete the job.

A working alone takes 8 hours more to complete the job than if both worked together. 
A takes (x+8) hours to complete the job.

If B worked alone, he would need 4.5 hours more to complete the job than they both working together.  
B takes (x+4.5) hours to complete the job.

They take x hours to complete the job together. 
1/(x+8) + 1/(x+4.5) = 1/x
2x^2 + 12.5x = (x+8)(x+4.5) = x^2 + 12.5x + 36
x^2 = 36
x = 6 hours

They will take 6 hours to complete the work together.

IMO C

krishna_sunder_ · Answer

Bunuel   sujoykrdatta

RATE         *            TIME             =WORK

a+b                          x                 =1
a                              x+8             =1
b                              x+4.5          =1

therefore
(a+b)x = a(x+8) => Bx = 8A    --------------1
the same way
(a+b)x = b(x+4.5) => Ax = 4.5B  ---------------2

multiplying 1 and 2
we get

(B*x) * (A*x) = (8*A)*(4.5*B)
A*B cancel's out in both sides giving

x*x = 8*4.5
x = 6

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=83555 Harsha GMAT-Club-Forum-lkw3mpl4.png

placeat · Answer

root of a.b = root8*4.5 =root 36 =6

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards