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# Jason can stack two shelves in 3 hours and Maria can stack three shelv

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Math Expert
Joined: 02 Sep 2009
Posts: 51073
Jason can stack two shelves in 3 hours and Maria can stack three shelv  [#permalink]

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28 Jul 2017, 07:55
1
2
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:36) correct 17% (01:54) wrong based on 115 sessions

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Jason can stack two shelves in 3 hours and Maria can stack three shelves in 2 hours. How long will it take them together, working at a constant rate, to stack thirteen shelves?

A. 5 hours
B. 6 hours
C. 6.5 hours
D. 11 hours
E. 12 hours

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Re: Jason can stack two shelves in 3 hours and Maria can stack three shelv  [#permalink]

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28 Jul 2017, 08:01
Bunuel wrote:
Jason can stack two shelves in 3 hours and Maria can stack three shelves in 2 hours. How long will it take them together, working at a constant rate, to stack thirteen shelves?

A. 5 hours
B. 6 hours
C. 6.5 hours
D. 11 hours
E. 12 hours

Jason = $$\frac{3}{2}$$ Shelves/Hour

Maria = $$\frac{2}{3}$$ Shelves/Hour

Together Jason and MAria = 3/2 + 2/3 = 13/6 Shelves/Hour

Time taken for 13 shelves working together = $$\frac{13}{{13/6}}$$ = 6 Hours

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Re: Jason can stack two shelves in 3 hours and Maria can stack three shelv  [#permalink]

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28 Jul 2017, 10:09
13/(2/3+3/2).
This yields 6.

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Re: Jason can stack two shelves in 3 hours and Maria can stack three shelv  [#permalink]

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29 Jul 2017, 23:32
1
Bunuel wrote:
Jason can stack two shelves in 3 hours and Maria can stack three shelves in 2 hours. How long will it take them together, working at a constant rate, to stack thirteen shelves?

A. 5 hours
B. 6 hours
C. 6.5 hours
D. 11 hours
E. 12 hours

J 2 shelves 3 hrs = 4 shelves 6 hrs
M 3 shelves 2 hrs= 9 shelves 6 hrs

J+M = 13 shelves 6 hrs

B
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Re: Jason can stack two shelves in 3 hours and Maria can stack three shelv  [#permalink]

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30 Jul 2017, 00:47
If Jason can stack 2 shelves in 3 hours,
he could stack a shelf in 1.5 hours, or in an hour he would have completed $$\frac{2}{3}$$rd(0.67) of the shelf.
Similarly, since Maria can stack 3 shelves in 2 hours, so she would complete $$1\frac{1}{2}$$(1.5) shelves in an hour.

Together, they would complete $$2\frac{1}{6}$$th(2.17) shelf in an hour, and it would take them 6 hours to do 13 shelves(Option B)

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Joined: 28 Jun 2017
Posts: 27
Location: India
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Re: Jason can stack two shelves in 3 hours and Maria can stack three shelv  [#permalink]

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31 Jul 2017, 13:09
1
It takes Jason 3hrs to stack 2 shelves
therefore he stacks 1 shelf in 1.5 hrs
It takes Maria 2 hrs to stack 3 shelves
Therefore she stacks 1 shelf in 0.66 hrs
Total shelves to be stacked = 13
Therefore time taken to stack 13 shelves= 13/(1.5+0.66) ~ 6
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Re: Jason can stack two shelves in 3 hours and Maria can stack three shelv  [#permalink]

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20 Aug 2018, 10:49
Bunuel wrote:
Jason can stack two shelves in 3 hours and Maria can stack three shelves in 2 hours. How long will it take them together, working at a constant rate, to stack thirteen shelves?

A. 5 hours
B. 6 hours
C. 6.5 hours
D. 11 hours
E. 12 hours

The combined rate of Jason and Maria is 2/3 + 3/2 = 4/6 + 9/6 = 13/6.

So it takes them 13/(13/6) = 13 x 6/13 = 6 hours to stack 13 shelves.

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Re: Jason can stack two shelves in 3 hours and Maria can stack three shelv &nbs [#permalink] 20 Aug 2018, 10:49
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