Problem Solving

It takes James 2 hours to mow a lawn and Fred 3 hours to mow the same lawn. How many hours would it take both men working simultaneously at their respective constant rates, to mow the lane?

• A. 5/6
  B. 1
  C. 6/5
  D. 5/6
  E. 5

James rate 1/2

Fred rate 1/3

James + Fred 1/2 + 1/3 = 5/6

Time required by both = 1/5/6 = 6/5

:p

1/2 + 1/3 = 5/6 of work in 1 hour.
To complete the work, the time required will be 6/5 hours.

IMO C
Best way to tackle work related problems is to use basic formula RT=D , where R= rate, T= time and D = work

Rj(2) = 1
Rf(3) = 1

When James and Fred work together, their respective rate gets added

So, (Rj+Rf)* T =1
(1/2 + 1/3)* T = 1
(5/6)* T =1
T = 6/5

Its the normal logic we use in the work related problem.... answer is 6/5[/url]

i would answer c and 6/5 if a word selected in the text would be replaced with the word 'together' likewise, speed of James 1/2 and speed of Fred 1/3; their combined speed 1/2 + 1/3 =5/6 and the time spend for a job is 1 : 5/6 or 6/5

BUT it says simultaneously, hence 5 and e

sivaelectric wrote:It takes James 2 hours to mow a lawn and Fred 3 hours to mow the same lawn. How many hours would it take both men working simultaneously at their respective constant rates, to mow the lane?

• A. 5/6
  B. 1
  C. 6/5
  D. 5/6
  E. 5

sivaelectric wrote:It takes James 2 hours to mow a lawn and Fred 3 hours to mow the same lawn. How many hours would it take both men working simultaneously at their respective constant rates, to mow the lane?

• A. 5/6
  B. 1
  C. 6/5
  D. 5/6
  E. 5

Hi,

there's a very simple formula to solve 2-worker problems:

Combined Time = (t1*t2)/(t1+t2)

So, we simply have:

CT = (2*3)/(2+3) = 6/5

That formula is derived from the more standard work formula:

1/(combined time) = 1/t1 + 1/t2+ 1/t3 + ...

in which t1, t2, t3 and so on are the times it takes individual workers to complete a job.

pemdas wrote:i would answer c and 6/5 if a word selected in the text would be replaced with the word 'together' likewise, speed of James 1/2 and speed of Fred 1/3; their combined speed 1/2 + 1/3 =5/6 and the time spend for a job is 1 : 5/6 or 6/5

BUT it says simultaneously, hence 5 and e

Hi,
'simultaneously' means 'at the same time'. Why will it be '5'?

If you and me work on the same project BUT we aren't told to work together - ONLY at the same time (simultaneously); it takes you 2 hours and me 3 hours. How long will it take both of us to work through the same job? I guess I will be spending 2 hours of my time and you need to spend 3 hours of your time. It should take us 5 hours to complete the same job, agree?

look options a and d are identical even

@seva, please reveal the source and OA

it must be mistake in this q. I tend to select c but the text is asking for e

Stuart Kovinsky wrote: 1/(combined time) = 1/t1 + 1/t2+ 1/t3 + ...

in which t1, t2, t3 and so on are the times it takes individual workers to complete a job.

I used exactly this approach above where 1/t1 + 1/t2+ 1/t3 + ... is combined speed and

1/(combined time) = combined speed (by allowing 1 as the whole or ONE job)

sivaelectric wrote:It takes James 2 hours to mow a lawn and Fred 3 hours to mow the same lawn. How many hours would it take both men working simultaneously at their respective constant rates, to mow the lane?

• A. 5/6
  B. 1
  C. 6/5
  D. 5/6
  E. 5

The answer to these is always the reciprocal of the sum of the fractions.

pemdas wrote:If you and me work on the same project BUT we aren't told to work together - ONLY at the same time (simultaneously); it takes you 2 hours and me 3 hours. How long will it take both of us to work through the same job? I guess I will be spending 2 hours of my time and you need to spend 3 hours of your time. It should take us 5 hours to complete the same job, agree?

it must be mistake in this q. I tend to select c but the text is asking for e

Hi,
I think your explanation is unnecessarily(unintentionally) misleading. The meaning of the question is working together. If both are working at the same time, why would it take 2 hours for one and 3 hours for the other. Let me try to explain this part. If it is taking 2 hours for one, that means you are assuming the other guy hasn't worked on that lawn for the 2 hours.Similarly, for the other. One more thing is if you are adding 2 hours and 3 hours, that means one has already done the work of mowing the lawn and then the second one is again doing the same after the first one has completed.
Even if the wording doesn't say working together, still 'working simultaneously' is closer in meaning to working together than 'one doing the work and then another doing the same work which has already been done'.

work=1

Thuse Rate james=1/2 and rate fred=1/3
total rate=5/6. work=1
time=6/5
IMO D

@Frankenstein, it was said - i tend for c

i understand wording may be confusing, and it is
e was off-price for this question and i keep c as the final answer
basically we are done with the same answer choice, as per my earliest explanation

sivaelectric wrote:It takes James 2 hours to mow a lawn and Fred 3 hours to mow the same lawn. How many hours would it take both men working simultaneously at their respective constant rates, to mow the lane?

• A. 5/6
  B. 1
  C. 6/5
  D. 5/6
  E. 5

John's Rate * time = work
John's Rate * 2 = 1
John's rate = 1/2

Similarly, Fred's rate is 1/3.

Their combined rate for one hour is:-
(1/2 + 1/3 ) * 1 = work
5/6 is the amount of work they can complete in one hour.

Total amount of work they need to complete is 1.

Therefore,

Rate * time = work
5/6 * time = 1

Solution: Time needed is 6/5

sivaelectric wrote:It takes James 2 hours to mow a lawn and Fred 3 hours to mow the same lawn. How many hours would it take both men working simultaneously at their respective constant rates, to mow the lane?

• A. 5/6
  B. 1
  C. 6/5
  D. 5/6
  E. 5

Let job = 6 units.
Rate for James = w/t = 6/2 = 3 units per hour.
Rate for Fred = w/t = 6/3 = 2 units per hour.
Combined rate for James and Fred = 3+2 = 5 units per hour.
Time for James and Fred to complete the job = w/r = 6/5 hours.

The correct answer is C.