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# Cheryl can paint a room in 4 hours, and David can paint the room in y

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Director
Joined: 12 Feb 2015
Posts: 917
Cheryl can paint a room in 4 hours, and David can paint the room in y  [#permalink]

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24 Mar 2019, 10:15
2
2
00:00

Difficulty:

25% (medium)

Question Stats:

77% (02:09) correct 23% (02:24) wrong based on 71 sessions

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Cheryl can paint a room in 4 hours, and David can paint the room in y hours. When Cheryl and David work together for $$\frac{5}{12}$$ of an hour, they can paint $$\frac{1}{6}$$ of the room. What is the value of y?

A) 4
B) $$\frac{20}{3}$$
C) $$\frac{37}{5}$$
D) $$\frac{15}{2}$$
E) 8

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Manish

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Re: Cheryl can paint a room in 4 hours, and David can paint the room in y  [#permalink]

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26 Mar 2019, 09:09
CAMANISHPARMAR wrote:
Cheryl can paint a room in 4 hours, and David can paint the room in y hours. When Cheryl and David work together for $$\frac{5}{12}$$ of an hour, they can paint $$\frac{1}{6}$$ of the room. What is the value of y?

A) 4
B) $$\frac{20}{3}$$
C) $$\frac{37}{5}$$
D) $$\frac{15}{2}$$
E) 8

rate of C = 1/4
rate of D= 1/y
combined rate = 1/6 = 5/12 * rate ; 2/5
so
1/4+1/y = 2/5
solve for y = 20/3
IMO B
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Re: Cheryl can paint a room in 4 hours, and David can paint the room in y  [#permalink]

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27 Mar 2019, 19:02
CAMANISHPARMAR wrote:
Cheryl can paint a room in 4 hours, and David can paint the room in y hours. When Cheryl and David work together for $$\frac{5}{12}$$ of an hour, they can paint $$\frac{1}{6}$$ of the room. What is the value of y?

A) 4
B) $$\frac{20}{3}$$
C) $$\frac{37}{5}$$
D) $$\frac{15}{2}$$
E) 8

Cheryl’s rate is 1/4, and David’s rate is 1/y. Their combined rate is (1/4 + 1/y). Using the formula: rate x time = work, we can create the equation:

(1/4 + 1/y)(5/12) = 1/6

5/48 + 5/(12y) = 1/6

Multiplying by 48y, we have:

5y + 20 = 8y

20 = 3y

20/3 = y

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Re: Cheryl can paint a room in 4 hours, and David can paint the room in y   [#permalink] 27 Mar 2019, 19:02
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