Multiple choice

Chris and Robert build a house in 45 days and 40 days, respectively. They began building the house together, but Chris leaves after some days and then, Robert completes the remaining construction in 23 days. Chris left the construction after how many days?

  1. 6

  2. 8

  3. 9

  4. 12

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Chris's rate = 1/45, Robert's rate = 1/40. Robert works alone for 23 days, completing 23/40 of the work. Remaining work = 1 - 23/40 = 17/40. They worked together for time T: T(1/45 + 1/40) = 17/40. T(8/360 + 9/360) = 17/40 => T(17/360) = 17/40 => T = 9 days.

AI explanation

Find the total work by taking the least common multiple of 45 and 40, which is 360 units. Chris works at 8 units per day and Robert works at 9 units per day. Robert works alone for 23 days to complete 207 units, meaning the remaining 153 units were completed when they worked together. Divide 153 by their combined speed of 17 units per day to find they worked together for 9 days.

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