When A works alone, it takes 14hrs, and when A works with B together,

Question

When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone?
 
A. 30hrs 
B. 33hrs 
C. 35hrs 
D. 37hrs 
E. 40hrs

ganand · Answer

Hi,

Note: Consider total amount of work as LCM of no. of hours required by different persons.

In this case, let's assume total amount of work = 70 units (LCM (14,10) = 70)

Rate of A work = 70/14 = 5 units/hr

Rate of A+B work = 70/10 = 7 units/hr

Rate of B work = 7 - 5 = 2 units/hr

The total amount of time required to complete the work by B = 70/2 = 35 hrs.

Answer: (C)

Thanks.

Klarbeinstreiter · Answer

Lets arrange the Information and assume that 1 unit of work needs to be done.

Work = Rate * Time
A: 1 = * 14
B: 1 = * T 
A+B: 1 = * 10

Now we fill in what we can deduct

Work = Rate * Time
A: 1 = 1/14 * 14
B: 1 = 1/T * T 
A+B: 1 = 1/10 * 10

What we need is T. If we add the rates of A and B we get the combined rate A+B.

(1/14) + (1/T) = (1/10)
=>(T+14 / 14T) = (1/10)
=>T+14 = (14T/10)
=>10T + 140 = 14T
=>140 = 4T 
=>T = 35

Answer C

Abhishek009 · Answer

Let the total work be = 70

Efficiency of A = 5
Efficiency of A + B = 7
So, Efficiency of B = 2

So, Time taken by B to work alone is  \frac{70}{2}  =  35  hours..

Thus, answer must be (C)

generis · Answer

There are a few ways to solve these problems. If possible, I find adding rates the easiest.

"It" is one job, or one unit of work.

(Rate of A and B together) - (rate of A) = (rate of B)

\frac{1}{10}  -  \frac{1}{14}  = \frac{(14 - 10)}{140}

=  \frac{4}{140}  =  \frac{1}{35}  --> B's rate

When work unit is one, flip the rate to get the time: 1/(1/35) = 35

Answer C

pclawong · Answer

Hello,
How do you assume A= 5?
Thank you very much

pushpitkc · Answer

Hi  pclawong ,

It is not so much as assumption in this case.
Here, the total units of work is 70 units and since A (when working alone) does the work in 14 hours,
A's efficieny is 70/14 = 5 units
Similarly, Since both do the work in 10 hours, their combined efficiency is 7 units.

This makes the efficiency of B(2 units), and the time it takes him to complete the work 35 hours(Option C)

Hope that helps you!

MathRevolution · Answer

==> For work rate questions, you solve “together and alone” reciprocally. It takes A 14hrs alone, and if you set the hours it took B to work alone as B hrs, from \((\frac{1}{14})+(\frac{1}{B})=\frac{1}{10}\) and \(\frac{1}{B}=(\frac{1}{10})-(\frac{1}{14})=\frac{1}{35}\), you get \(B=35\).

The answer is C.
Answer: C

The answer is C.
Answer: C

MBAHOUSE · Answer

When A works alone, it takes 14hrs, and when A works with B together, it takes 10hrs. How many hours does it take B to work alone?
 
A. 30hrs 
B. 33hrs 
C. 35hrs 
D. 37hrs 
E. 40hrs

When A works alone, it takes 14hrs, and when A works with B together,

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When A works alone, it takes 14hrs, and when A works with B together,

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