AMC 10 Weekly Practice Round 2
Complete problem set with solutions and individual problem pages
To build a water channel, Team can finish the job alone in days, and Team can finish it alone in days. If they work together, their efficiency decreases due to interference: Team ’s efficiency becomes of its original, and Team ’s efficiency becomes of its original. The plan is to complete the channel in days, with the goal of minimizing the number of days they work together. How many days should the two teams work together?
- A.
- B.
- C.
- D.
- E.
Team ’s individual work rate is , and Team ’s individual work rate is .
When working together, their combined work rate is:
To minimize the number of days they work together, the remaining work should be done by the faster Team .
Let be the number of days they work together.
Then:
Solving gives .
Therefore, the two teams need to work together for days.
