Question : Michelle can finish a work in 40 days. Carol can finish the same work in 41 days while Amanda can finish the work in 42 days. How long will it take to finish it if they work together?
Correct Answer 13 1667/2521 days or 13.661 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Michelle = 40 days
And, the number of days required to finish the same work by Carol = 41 days
And, the number of days required to finish the same work by Amanda = 42 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 40 days the work is done by Michelle = 1
∴ The work done by Michelle in 1 day = 1/40
Similarly,
∵ In 41 days the work is done by Carol = 1
∴ The work done by Carol in 1 day = 1/41
Similarly,
∵ In 42 days the work is done by Amanda = 1
∴ The work done by Amanda in 1 day = 1/42 part
Now, the work done by Michelle, Carol, and Amanda together in 1 day
= Michelle's 1 day work + Carol's 1 day work + Amanda's 1 day work
= 1/40 + 1/41 + 1/42
= 861 + 840 + 820/34440
= 2521/34440 part of work
This means in 1 day, 2521/34440 part of work is done by Michelle, Carol and Amanda working together.
Now, the number of days required to finish 2521/34440 part of work by Michelle, Carol, and Amanda working together = 1
∴ the number of days required to finish the whole work (1 work) by Michelle + Carol + Amanda together
= 1/2521/34440
= 1 × 34440/2521 = 34440/2521 days
= 13 1667/2521 days = or 13.661 days
Thus, Michelle, Carol, and Amanda working together will finish the total work (1 work) in 13 1667/2521 days = or 13.661 days Answer
Shortcut Trick to solve the problems based on time and work using formula
Case: If A can finish a work in a days, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= a × b × c/ab + ac + bc days.
Here given,
The number of days required to finish the work by Michelle = 40 days
And the number of days required to finish the same work by Carol = 41 days
And the number of days required to finish the work by Amanda = 42 days
Thus, the number of days required to finish the work by Michelle, Carol, and Amanda together = ?
Here a = 40 days
And, b = 41 days
And, c = 42 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Michelle, Carol, and Amanda working together
= 40 × 41 × 42/40 × 41 + 40 × 42 + 41 × 42 days
= 68880/1640 + 1680 + 1722 days
= 68880/5042 days
= 68880/5042 days
= 68880 ÷ 2/5042 ÷ 2 = 34440/2521 days
= 13 1667/2521 days or 13.661
Thus, Michelle, Carol, and Amanda together will finish the work in 13 1667/2521 days or 13.661 days Answer
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