Multiple choice

Two workers, Sarah and David, are paid \$600 together for completing a task. If Sarah works for 8 days and David works for 6 days, they can complete the task. If Sarah works for 12 days, she alone can complete the task. How should the \$600 be divided between Sarah and David?

  1. $350 and $250
  2. $375 and $225
  3. $400 and $200
  4. $425 and $175
  5. $450 and $150
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sarah completes the task in 12 days, so her daily rate is 1/12. In 8 days, Sarah does 8/12 = 2/3 of the work. David does the remaining 1/3 in 6 days, so his daily rate is (1/3) / 6 = 1/18. The payment should be proportional to work done: Sarah does 2/3 and David does 1/3. Thus, Sarah gets 2/3 of 600 = 400 and David gets 1/3 of 600 = 200.

AI explanation

If Sarah takes 12 days alone, her work rate is 1/12 of the task per day. Since Sarah and David finish it in 8 and 6 days respectively, Sarah completes 8/12 (or 2/3) of the task, leaving 1/3 of the task for David. The \$600 should be divided in the ratio of work completed, which is (2/3) to (1/3), or 2 to 1; therefore, Sarah receives \$400 and David receives $200.

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