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Helen and Sergey must cut down a row of trees. Helen can cut

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Helen and Sergey must cut down a row of trees. Helen can cut [#permalink] New post 09 Dec 2017, 18:44
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Helen and Sergey must cut down a row of trees. Helen can cut down the entire row in 3 hours, and Sergey can cut down the entire row in 7 hours. If they simultaneously start cutting trees, each starting at one end of the row and working towards each other, what fraction of the trees will Sergey have cut at the time they meet?

Drill 4
Question: 3
Page: 531


[Reveal] Spoiler: OA
\(\frac{3}{10}\) or 0.3

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Re: Helen and Sergey must cut down a row of trees. Helen can cut [#permalink] New post 10 Dec 2017, 18:18
Can someone please share the solution.
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Re: Helen and Sergey must cut down a row of trees. Helen can cut [#permalink] New post 10 Dec 2017, 19:04
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I dont know if my reasoning is right but I proceed as follows.
Let's pretend that the aforementioned row of trees is constitued of 21 trees.
Since Serguey needs 7 hours to cut the 21 trees, he has a rate of 3 trees per hour.
Helen needs only 3 hours, so she cuts 7 trees per hours.
Since they are approching, we must use the distance gap (21 trees) over their rates combined which is 10.
21/10 = 2,1.
Now we know that they will meet after 2 hours and 10 min.
But the question asks what is the portion of cut trees that Serguy would have done at the time they meet.
Since Serguy needs 7 hours to cut the 21 trees, he only did 2,1 hours for now. So the proportion is 2,1/7 which is 0,3.

I am pretty sure there is another shortcut to do this !
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Re: Helen and Sergey must cut down a row of trees. Helen can cut [#permalink] New post 15 Dec 2017, 03:45
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This is analogous to a distance-time-speed problem. Of course, you don't need to see it that way to solve the question but I think it's just good to be aware how you can relate concepts that are seemingly different.

H -> ................ <- S

Now the question can be understood in the following manner: H moves at 7 km/hr and S moves at 3 km/hr. When they meet, how much of the distance has S covered? Let's assume the distance is 21 km (divisible by both 3 and 7, probably your first instinct as a number). Recall when they meet, the time taken for both is equal

x / 7 = (21 - x) / 3

(At this point you will recognize that choosing a small number like 1 will probably be better than 21)

x = 14.7

So H covers 14.7 km, which means S covers 6.3 km.

The distance S covered as a ratio is 6.3 / 21 = 63 / 210 = 0.3. Again, this calculation is much quicker if you are smart with picking a distance value.

Probably not the quickest method, just the method I used.
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Re: Helen and Sergey must cut down a row of trees. Helen can cut [#permalink] New post 29 Dec 2017, 16:22
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Explanation

You don’t know how many trees there are, so define the job by plugging in an easy number, such as 21 trees.

Use rate pies to figure out that Helen’s rate is 7 trees/hr and Sergey’s rate is 3 trees/hr. That means their combined rate is 10 trees/hr. Put their combined rate into another
rate pie with the total trees to find it takes them \(\frac{21}{10}\) or 2.1 hours to meet.

To find out how many trees Sergey has cut down at this point, put his individual rate into another rate pie with 2.1 hours. 3 trees/hr × 2.1 hours = 6.3 trees at the point they meet. Put the number of trees Sergey has cut when they meet over the total trees: \(\frac{63}{21}=\frac{3}{10}\), so the correct answer is \(\frac{3}{10}\) or 0.3.
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Re: Helen and Sergey must cut down a row of trees. Helen can cut [#permalink] New post 26 Jan 2018, 07:52
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sandy wrote:
Helen and Sergey must cut down a row of trees. Helen can cut down the entire row in 3 hours, and Sergey can cut down the entire row in 7 hours. If they simultaneously start cutting trees, each starting at one end of the row and working towards each other, what fraction of the trees will Sergey have cut at the time they meet?

Drill 4
Question: 3
Page: 531


[Reveal] Spoiler: OA
\(\frac{10}{3}\) or 0.3

just a little correction ans has 10/3 instead of 3/10
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Re: Helen and Sergey must cut down a row of trees. Helen can cut [#permalink] New post 26 Jan 2018, 09:14
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Fixed. Precious.

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Re: Helen and Sergey must cut down a row of trees. Helen can cut   [#permalink] 26 Jan 2018, 09:14
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