AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 27 Hard

Two projects of equal workload are completed separately by Team 1 and Team 2. On sunny days, Team 1 can finish a project in 12 days, and Team 2 can finish a project in 15 days. On rainy days, Team 1’s work efficiency decreases by 40\%, and Team 2’s work efficiency decreases by 10\%. In the end, the two teams finish their projects at the same time.

What is the difference between the number of sunny days and rainy days during the work period?

  • A.

    0

  • B.

    1

  • C.

    2

  • D.

    3

  • E.

    4

Answer:E

On sunny days, the work efficiencies of Team 1 and Team 2 are \frac{1}{12} and \frac{1}{15} respectively, so Team 1’s efficiency is higher by \frac{1}{12} - \frac{1}{15} = \frac{1}{60}.

On rainy days, their work efficiencies are \frac{1}{12} \times (1 - 40\%) = \frac{1}{20} and \frac{1}{15} \times (1 - 10\%) = \frac{3}{50} respectively, so Team 2’s efficiency is higher by \frac{3}{50} - \frac{1}{20} = \frac{1}{100}.

From \frac{\frac{1}{60}}{\frac{1}{100}} = 5 : 3 we know that in 3 sunny days and 5 rainy days, the progress of the two teams is the same.

During this time, they complete \frac{1}{12} \times 3 + \frac{1}{20} \times 5 = \frac{1}{2} of the work.

Therefore, during the construction period, there were 6 sunny days and 10 rainy days. The difference is 4.