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Jack works at a constant rate and he can produce a maximum of 5 units

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Jack works at a constant rate and he can produce a maximum of 5 units  [#permalink]

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New post 27 Sep 2018, 03:34
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  55% (hard)

Question Stats:

64% (02:54) correct 36% (02:53) wrong based on 45 sessions

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Jack works at a constant rate and he can produce a maximum of 5 units of a product in 4 hours. He is paid $4 per unit, for the first 20 units and $5.5 for each additional unit, that he produces on a particular day. If he earned $91 on the first day and $135 on the second day. What is the minimum time that Jack had worked on these two days combined?

    A. 17 hours 36 minutes
    B. 39 hours 12 minutes
    C. 41 hours 36 minutes
    D. 42 hours
    E. 44 hours

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Re: Jack works at a constant rate and he can produce a maximum of 5 units  [#permalink]

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New post 27 Sep 2018, 10:05
5 units = 4 hr ; 1 unit = 4/5hr
91$ = 20 units * 4 + 2 units * 5.5
Time taken = 22*4/5 = 17.6 = 17hr 36 min

135$ = 20 units * 4 + 10 units * 5.5
Time taken = 30*4/5 = 24 hr

Total time = 41hr 36 mins
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Jack works at a constant rate and he can produce a maximum of 5 units  [#permalink]

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New post 03 Oct 2018, 05:05

Solution


Given:
    • Jack works at a constant rate and he can produce 5 products at max in 4 hours
    • For the first 20 units of product, he gets $4 per unit
    • For each additional unit that he produces, he gets $5.5 per unit
    • He earned $91 on the first day and $135 on the second day

To find:
    • The minimum time that Jack had worked on these two days combined

Approach and Working:
As Jack can produce maximum 5 units in 4 hours, in 1 hour he can produce 5/4 units.
    • If Jack has produced 20 units of the product on a day, he earns 20 * $4 = $80 on that day.
    • If the amount earned is greater than $80, then it means he had produced more than 20 units.
      o In such case, he earns $5.5 for each additional unit.
      o Thus, we can find the number of additional units by dividing the remaining amount by $5.5

On first day:
    • Jack earned $91, which is > $80,
      o Thus, number of additional units produced = \(\frac{($91 - $80)}{$5.5} = \frac{$11}{$5.5}= 2\)

    • So, total units produced by Jack = 20 + 2 = 22
    • Minimum time taken = \(22 * \frac{24 hours}{(the maximum number of products that Jack produce in one day)} = 22 * \frac{24 hours}{30} = 17.6 hours = 17 hours 36 minutes\)

On second day:
    • Jack earned $135, which is > $80,
      o Thus, number of additional units produced = \(\frac{($135 - $80)}{$5.5} = \frac{$55}{$5.5} = 10\)

    • So, total units produced by Jack = 20 + 10 = 30
      o 30 is the maximum number of units that he can produce in a day \(5 units * \frac{(24 hours)}{(4 hours)}\)
      o Thus, minimum time taken = 24 hours

Therefore, total minimum time taken = 17 hours 36 minutes + 24 hours = 41 hours 36 minutes

Hence, the correct answer is Option C

Answer: C

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Jack works at a constant rate and he can produce a maximum of 5 units &nbs [#permalink] 03 Oct 2018, 05:05
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