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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

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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

by Gmat_mission » Sun Jun 14, 2020 1:55 pm

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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?

A. 1/10
B. 3/10
C. 3/7
D. 4/7
E. 7/10

[spoiler]OA=B[/spoiler]

Source: Princeton Review
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Re: 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

by Scott@TargetTestPrep » Tue Jun 23, 2020 8:26 am
Gmat_mission wrote: ↑
Sun Jun 14, 2020 1:55 pm
 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?

A. 1/10
B. 3/10
C. 3/7
D. 4/7
E. 7/10

[spoiler]OA=B[/spoiler]

Solution:

We can assume there are 21 trees. So Helen’s rate is 21/3 = 7 trees per hour and Sergey’s rate is 21/7 = 3 trees per hour. We can create the equation where x is the number of hours it takes to cut down all 21 trees when they work together:

7x + 3x = 21

10x = 21

x = 2.1

In 2.1 hours Sergey cuts 3 * 2.1 = 6.3 trees, which is 6.3/21 = 63/210 = 3/10 of the trees.

Answer: B

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