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# It takes John 3 hours to assemble a model plane. Working together Mike

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
It takes John 3 hours to assemble a model plane. Working together Mike  [#permalink]

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25 Jul 2018, 23:04
00:00

Difficulty:

5% (low)

Question Stats:

92% (00:36) correct 8% (01:39) wrong based on 38 sessions

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It takes John 3 hours to assemble a model plane. Working together, Mike and John take 2 hours to assemble the model plane. How long would it take Mike working alone to assemble the plane?

A. 2
B. 3
C. 4
D. 5
E. 6

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Joined: 31 Oct 2013
Posts: 898
Concentration: Accounting, Finance
GPA: 3.68
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Re: It takes John 3 hours to assemble a model plane. Working together Mike  [#permalink]

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26 Jul 2018, 00:33
Bunuel wrote:
It takes John 3 hours to assemble a model plane. Working together, Mike and John take 2 hours to assemble the model plane. How long would it take Mike working alone to assemble the plane?

A. 2
B. 3
C. 4
D. 5
E. 6

John works in 1 hour = 1/3

john and mike work in 1 hour = 1/2

mike work in 1 hour = 1/2 - 1/3 = 1/6

So, mike needs 6 hrs to assemble the plane.

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Re: It takes John 3 hours to assemble a model plane. Working together Mike  [#permalink]

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26 Jul 2018, 10:14
Bunuel wrote:
It takes John 3 hours to assemble a model plane. Working together, Mike and John take 2 hours to assemble the model plane. How long would it take Mike working alone to assemble the plane?

A. 2
B. 3
C. 4
D. 5
E. 6

Let the total work be 6 units.

SO, Efficiency of John = 2units/hr and Combined efficiency of John and Mike is 3 units/hr

Thus, efficiency of Mike is 1 unit/hr

Hence, Time required for Mike to complete the job is 6 hours, answer must be (E)
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It takes John 3 hours to assemble a model plane. Working together Mike  [#permalink]

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27 Jul 2018, 09:16
Bunuel wrote:
It takes John 3 hours to assemble a model plane. Working together, Mike and John take 2 hours to assemble the model plane. How long would it take Mike working alone to assemble the plane?

A. 2
B. 3
C. 4
D. 5
E. 6

Use TIME formula

Formula for total time needed for A and B, working simultaneously, to finish the job

$$\frac{AB}{A+B}=T_{(A+B)}$$

$$A$$ = John's time = $$3$$
$$B$$ = Mike's time = $$M$$
$$T$$ = Total time = $$T_{(A+B)}=2$$

$$\frac{AB}{A+B}=T_{(A+B)}$$

$$\frac{3*M}{3+M}=2$$
$$3M=2(3+M)$$
$$3M=6 +2M$$
$$M=6$$

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Re: It takes John 3 hours to assemble a model plane. Working together Mike  [#permalink]

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30 Jul 2018, 10:28
Bunuel wrote:
It takes John 3 hours to assemble a model plane. Working together, Mike and John take 2 hours to assemble the model plane. How long would it take Mike working alone to assemble the plane?

A. 2
B. 3
C. 4
D. 5
E. 6

John’s rate is 1 plane in 3 hours, or 1/3, and we will let Mike’s rate be 1 plane in M hours, or 1/M. Since they can complete a plane in 2 hours when they work together, their combined rate is 1/2.Thus, we can create the equation:

1/3 + 1/M = 1/2

Multiplying by 6M we have:

2M + 6 = 3M

6 = M

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Re: It takes John 3 hours to assemble a model plane. Working together Mike &nbs [#permalink] 30 Jul 2018, 10:28
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