AMC 10 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 9 Medium

A construction team was originally scheduled to lay a water pipeline in 18 days. After working for 6 days, two-thirds of the team was reassigned to other tasks. How many total days will it take to complete the pipeline?

  • A.

    24

  • B.

    30

  • C.

    36

  • D.

    27

  • E.

    42

Answer:E

Let the total work required be "1" unit. The original team's daily work rate is 1 \div 18 = \frac{1}{18}. After working for 6 days, they have completed \frac{1}{18} \times 6 = \frac{1}{3} of the total work. When two-thirds of the team is reassigned, the remaining team's efficiency is reduced to 1 - \frac{2}{3} = \frac{1}{3}, so their new work rate is \frac{1}{18} \times \frac{1}{3} = \frac{1}{54}. The remaining work to be done is 1 - \frac{1}{3} = \frac{2}{3}, and at the new work rate, it will take \frac{2}{3} \div \frac{1}{54} = 36 days to complete the remaining work. Therefore, the total time required to complete the pipeline is 6 + 36 = 42 days.

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