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Jenny takes 3 hours to sand a picnic table; Laila can do the same job

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Bunuel
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Jenny takes 3 hours to sand a picnic table; Laila can do the same job [#permalink] New post   21 Jun 2018, 02:42
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Jenny takes 3 hours to sand a picnic table; Laila can do the same job in \(\frac{1}{2}\) hour. Working together at their respective constant rates, Jenny and Laila can sand a picnic table in how many hours?


(A) \(\frac{1}{6}\)

(B) \(\frac{2}{9}\)

(C) \(\frac{1}{3}\)

(D) \(\frac{3}{7}\)

(E) \(\frac{5}{6}\)
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D
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Re: Jenny takes 3 hours to sand a picnic table; Laila can do the same job [#permalink] New post   21 Jun 2018, 03:37
Bunuel wrote:
Jenny takes 3 hours to sand a picnic table; Laila can do the same job in \(\frac{1}{2}\) hour. Working together at their respective constant rates, Jenny and Laila can sand a picnic table in how many hours?


(A) \(\frac{1}{6}\)

(B) \(\frac{2}{9}\)

(C) \(\frac{1}{3}\)

(D) \(\frac{3}{7}\)

(E) \(\frac{5}{6}\)


Jenny speed= \(\frac{1}{3}\) pincinc table/hour
Laila speed= \(2\) pincinc table/hour
Total speed together= \(2+\frac{1}{3}=\frac{7}{3}\) table/hour
Time to prepare a table= 1/ Total speed= \(\frac{3}{7}\) --> ANSWER D
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Re: Jenny takes 3 hours to sand a picnic table; Laila can do the same job [#permalink] New post   21 Jun 2018, 03:37
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Let's assume a certain unit of work required, say 3*(1/2)=1.5 units of work.

Jenny requires 3 hours to complete 1.5 units of work, so her work rate is 1.5/3 = 0.5 units/hour.
Laila requires 1/2 hour to complete 1.5 units of work, so her work rate is 1.5/(1/2) = 3 units/hour.

Together their work rate is 3.5 units per hour.

1.5/3.5 is 3/7.

Answer is D.
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Re: Jenny takes 3 hours to sand a picnic table; Laila can do the same job [#permalink] New post   21 Jun 2018, 06:51
Expert Reply

Solution



Given:
    • Jenny takes 3 hours to sand a picnic table
    • Laila can do the same job in 1/2 hour

To find:
    • Jenny and Laila, together can sand a picnic table in how many hours.

Approach and Working:

    • Let the total work is of 3 units.
      o Then, Jenny does 1 unit of work in 1 hour.
      o And Laila does 6 unit of work in 1 hour or 3 units of work in ½ hour.
    • Together they will do 7 unit in 1 hour.
    • So to complete 3 units of work they will take 3/7 hours.

Hence, the correct answer is option D.

Answer: D
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Re: Jenny takes 3 hours to sand a picnic table; Laila can do the same job [#permalink] New post   22 Jun 2018, 02:58
Bunuel wrote:
Jenny takes 3 hours to sand a picnic table; Laila can do the same job in \(\frac{1}{2}\) hour. Working together at their respective constant rates, Jenny and Laila can sand a picnic table in how many hours?


(A) \(\frac{1}{6}\)

(B) \(\frac{2}{9}\)

(C) \(\frac{1}{3}\)

(D) \(\frac{3}{7}\)

(E) \(\frac{5}{6}\)



Apply in the following:

Time combined = A * B/ (A+B) = \(\frac{3}{2}\)/ \(\frac{7}{2}\) = \(\frac{3}{7}\)

Answer: D
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Re: Jenny takes 3 hours to sand a picnic table; Laila can do the same job [#permalink] New post   01 Nov 2021, 07:34
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Re: Jenny takes 3 hours to sand a picnic table; Laila can do the same job [#permalink]
01 Nov 2021, 07:34
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