Multiple choice

Tamal and Tina can independently complete a certain job in four days and nine days respectively. They together started the work, but after two days both left and the remaining work was completed by Trisha in two more days. How long, in days, will Trisha alone complete the entire job?

  1. 7.2

  2. 8

  3. 12

  4. Cannot be determined
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A Correct answer
Explanation

Tamal's rate is 1/4 per day, Tina's is 1/9 per day. Combined rate is 1/4 + 1/9 = 13/36. In 2 days, they complete 2 * (13/36) = 13/18 of the work. Remaining work is 5/18. Trisha completes 5/18 in 2 days, so her rate is (5/18) / 2 = 5/36 per day. Time for Trisha to finish the whole job is 36/5 = 7.2 days.

AI explanation

Tamal and Tina's one day's work is 1/4 and 1/9 respectively. Their combined one day's work is 1/4 + 1/9 = 13/36, so in two days they complete 26/36 = 13/18 of the work. The remaining work is 1 - 13/18 = 5/18, which Trisha completes in 2 days. Trisha's 1-day work is (5/18) / 2 = 5/36, meaning she alone requires 36 / 5 = 7.2 days to complete the entire job.

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