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Ali and Moe can do a certain job together in 4 hours and Ali is 5 time

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Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 07 May 2017, 13:47
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Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes

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Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post Updated on: 07 May 2017, 20:48
1
Rate at which Ali works = 1/a
Rate at which Moe works = 1/m

(1/a + 1/m) * 4 = 1

1/a = 5 * 1/m

(1/a + 1/5a) * 4 = 1

6*4/5a = 1

a = 24/5 hours = 4.8 hours = 4 hours 48 minutes

Answer is C. 4 hours 48 minutes

Originally posted by quantumliner on 07 May 2017, 15:00.
Last edited by quantumliner on 07 May 2017, 20:48, edited 1 time in total.
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 07 May 2017, 16:20
Let us assume the total work which needs to be done is 120 units (LCM of 4,5 and 6 which are basically the numbers used in the question).
Therefore, the work completed by Ali and Moe in 1 hour = 120 units/4 hours i.e. 30 units/hour.
Now, we know that Ali is 5 times faster than Moe. So, if the total work was 30 units/hour, Ali would finish 25 units and Moe, 5 units.
So, if Ali were to finish the task alone, he'll need to finish 120 units at a rate of 25 units/hour. i.e. 120 units/ 25 units = 4.8 which translates to 4 hours and 48 minutes.
Hence, option C is the correct answer.

Hope it helps :)
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 07 May 2017, 16:30
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quantumliner wrote:
Rate at which Ali works = 1/a
Rate at which Moe works = 1/m

(1/a + 1/m) * 4 = 1

1/a = 5 * 1/m

(1/a + 1/5a) * 4 = 1

6*4/5a = 1

a = 24/5 hours = 4.2 hours = 4 hours 12 minutes

Answer is B. 4 hours 12 minutes



Could you please help me with understanding your approach?
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 07 May 2017, 16:52
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Let M's speed = s
A's speed = 5s
Combined speed = 6s, time taken to complete work = 4 hours.
Hence total work = speed * time = 6s * 4 = 24s
Now, if only A does the work, then time taken = total work/speed of A = 24s/5s = 24/5 hours = 4 hours 48 mins.
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 07 May 2017, 23:20
Total work : 120 units
Both can do the work in 4 hours(Rate of combined work is 30 units/hr)
Let the rate of Moe be x, hence rate of Ali is 5x. Combined rate is 6x.
Equating the two, x=5units
Time taken by Moe alone to do the work is 24/5 = 4 hours 4/5*60 mins or 4 hours 48 minutes(Option C)

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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 08 May 2017, 04:22
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Let time taken by Ali = x hours
time taken by Moe= 5x hours

Work done by both of them in 1 hour:

\(\frac{1}{x}\) + \(\frac{1}{5x}\)= \(\frac{1}{4}\)

\(\frac{5 +1}{5x}\) =\(\frac{1}{4}\)

\(\frac{6}{5x}\)= \(\frac{1}{4}\); x= \(\frac{24}{5}\); x= 4\(\frac{4}{5}\) or 4 hour 48 mins

Thus, Time taken by Ali= 4 hours 48 mins.

Answer: C.

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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 08 May 2017, 07:37
Bunuel wrote:
Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes


Ali + Moe = \(\frac{1}{4}\) of a job an hour

Ali = 5 Moes (5M)

Ali + Moe = 6 Moes (6M)

Ali + Moe = 6M = \(\frac{1}{4}\) of a job an hour

1 Moe = \(\frac{1}{24}\) of a job an hour

Ali = 5 Moes = \(\frac{5}{24}\) of a job an hour

\(\frac{24}{5}\) = 4 \(\frac{4}{5}\) hours

4 \(\frac{4}{5}\) hours = 4.48 hours (C)
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 18 Nov 2018, 19:40
Bunuel wrote:
Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes


let r=A's rate
r+r/5=1/4→
r=5/24
inverting, A's time=24/5=4 hours and 48 minutes
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 19 Nov 2018, 00:27
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Bunuel wrote:
Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes


Using ratios:
Ali is 5 times faster so if Moe's rate of work is R, Ali's is 5R. Their combined rate of work is 6R.

If the rate of work becomes 5R (only Ali working), time taken will be inverse i.e. in the ratio 5:6.
So time taken will be 1/5th more than 4 hrs i.e. 4 + 4*(1/5) = 4 hrs 48 mins

Answer (C)
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 19 Nov 2018, 01:29
If Moeen's speed = x
Then Ali's speed = 5x

When both work together, their total speed = 6x
And the time taken to complete work = 4 hours i.e. 240 minutes

Now, if only Ali does the work, then speed be = 5x
Since speed has reduced, the total time will go up as the total work remains constant.
Hence -->
\(6x * 240 = 5x * T\)
=> T = \(6x * 240 / 5x\)
=> = 288
=> = 4 hours 48 minutes

Hence C is the correct answer
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 19 Nov 2018, 01:39
Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes

In 1 hour Moe can do 1/x part of the job and Ali can do 5/x part of the job (Since Ali is 5 times faster than Moe).
=> in 1 hour they can do (1/x+5/x) part of the job. Since they can complete the job in 4 hours, then we can say that 4*(1/x+5/x)=1
From the equation above we find that x=24.
=> In 1 hour Ali can do 5/24 part of the job, so he needs 24/5 hour to complete the job.
24/5 = 4 4/5 = 4 hours 48 minutes (C)
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 30 Mar 2019, 02:06
VeritasKarishma wrote:
Using ratios:
Ali is 5 times faster so if Moe's rate of work is R, Ali's is 5R. Their combined rate of work is 6R.

If the rate of work becomes 5R (only Ali working), time taken will be inverse i.e. in the ratio 5:6.
So time taken will be 1/5th more than 4 hrs i.e. 4 + 4*(1/5) = 4 hrs 48 mins

Answer (C)

Please VeritasKarishma ,
I am a little confused about the word meaning.

if "Ali is 5 times faster than Moe", doesn't it mean that A = M + 5M, so A = 6M ?
I thought that "more than" means to add. so the combined work would be 7R
I wish you can clarify this to me.
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 30 Mar 2019, 23:06
Mahmoudfawzy83 wrote:
VeritasKarishma wrote:
Using ratios:
Ali is 5 times faster so if Moe's rate of work is R, Ali's is 5R. Their combined rate of work is 6R.

If the rate of work becomes 5R (only Ali working), time taken will be inverse i.e. in the ratio 5:6.
So time taken will be 1/5th more than 4 hrs i.e. 4 + 4*(1/5) = 4 hrs 48 mins

Answer (C)

Please VeritasKarishma ,
I am a little confused about the word meaning.

if "Ali is 5 times faster than Moe", doesn't it mean that A = M + 5M, so A = 6M ?
I thought that "more than" means to add. so the combined work would be 7R
I wish you can clarify this to me.


Mahmoudfawzy83,

I understand where you are coming from but five times faster has come to mean 5X over time.
"5 times faster" is the accepted way of expressing "X becomes 5X".
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 31 Mar 2019, 01:31
Bunuel wrote:
Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes


together rate
a+m/am= 1/4
and 1/a = 5*1/m and m = 5a
so
6a/5a^2= 1/4
solve a= 24/5 ;4.8 hrs or say 4 hrs and 48 mins
IMO C
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time   [#permalink] 31 Mar 2019, 01:31
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