AMC 10 Weekly Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 29 Hard

Teams A and B are responsible for a project. At the normal rate of work, it would take 60 days to complete. Now, Team A’s efficiency increases by one-half, and Team B’s efficiency decreases by one-half, and the project takes 84 days to finish. How many days would it take Team A alone to complete the project?

  • A.

    230

  • B.

    250

  • C.

    260

  • D.

    280

  • E.

    290

Answer:D

Let Team A’s work rate be a and Team B’s work rate be b.

We then have the system of equations:

\begin{cases} a + b = \frac{1}{60} \\ 1.5a + 0.5b = \frac{1}{84} \end{cases}

Solving gives:

\begin{cases}a = \frac{1}{280} \\b = \frac{11}{840}\end{cases}

Thus, Team A’s work rate is \frac{1}{280}, meaning Team A alone would take 280 days to complete the project.

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