Question : Amanda can finish a work in 44 days. Dorothy can finish the same work in 45 days while Melissa can finish the work in 46 days. How long will it take to finish it if they work together?
Correct Answer 14 3022/3037 days or 14.995 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Amanda = 44 days
And, the number of days required to finish the same work by Dorothy = 45 days
And, the number of days required to finish the same work by Melissa = 46 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 44 days the work is done by Amanda = 1
∴ The work done by Amanda in 1 day = 1/44
Similarly,
∵ In 45 days the work is done by Dorothy = 1
∴ The work done by Dorothy in 1 day = 1/45
Similarly,
∵ In 46 days the work is done by Melissa = 1
∴ The work done by Melissa in 1 day = 1/46 part
Now, the work done by Amanda, Dorothy, and Melissa together in 1 day
= Amanda's 1 day work + Dorothy's 1 day work + Melissa's 1 day work
= 1/44 + 1/45 + 1/46
= 1035 + 1012 + 990/45540
= 3037/45540 part of work
This means in 1 day, 3037/45540 part of work is done by Amanda, Dorothy and Melissa working together.
Now, the number of days required to finish 3037/45540 part of work by Amanda, Dorothy, and Melissa working together = 1
∴ the number of days required to finish the whole work (1 work) by Amanda + Dorothy + Melissa together
= 1/3037/45540
= 1 × 45540/3037 = 45540/3037 days
= 14 3022/3037 days = or 14.995 days
Thus, Amanda, Dorothy, and Melissa working together will finish the total work (1 work) in 14 3022/3037 days = or 14.995 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 Amanda = 44 days
And the number of days required to finish the same work by Dorothy = 45 days
And the number of days required to finish the work by Melissa = 46 days
Thus, the number of days required to finish the work by Amanda, Dorothy, and Melissa together = ?
Here a = 44 days
And, b = 45 days
And, c = 46 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Amanda, Dorothy, and Melissa working together
= 44 × 45 × 46/44 × 45 + 44 × 46 + 45 × 46 days
= 91080/1980 + 2024 + 2070 days
= 91080/6074 days
= 91080/6074 days
= 91080 ÷ 2/6074 ÷ 2 = 45540/3037 days
= 14 3022/3037 days or 14.995
Thus, Amanda, Dorothy, and Melissa together will finish the work in 14 3022/3037 days or 14.995 days Answer
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