Question:
Amanda can finish a work in 48 days. Melissa can finish the same work in 53 days while Deborah can finish the work in 58 days. How long will it take to finish it if they work together?
Correct Answer
17 2359/4201 days or 17.562 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Amanda = 48 days
And, the number of days required to finish the same work by Melissa = 53 days
And, the number of days required to finish the same work by Deborah = 58 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 48 days the work is done by Amanda = 1
∴ The work done by Amanda in 1 day = 1/48
Similarly,
∵ In 53 days the work is done by Melissa = 1
∴ The work done by Melissa in 1 day = 1/53
Similarly,
∵ In 58 days the work is done by Deborah = 1
∴ The work done by Deborah in 1 day = 1/58 part
Now, the work done by Amanda, Melissa, and Deborah together in 1 day
= Amanda's 1 day work + Melissa's 1 day work + Deborah's 1 day work
= 1/48 + 1/53 + 1/58
= 1537 + 1392 + 1272/73776
= 4201/73776 part of work
This means in 1 day, 4201/73776 part of work is done by Amanda, Melissa and Deborah working together.
Now, the number of days required to finish 4201/73776 part of work by Amanda, Melissa, and Deborah working together = 1
∴ the number of days required to finish the whole work (1 work) by Amanda + Melissa + Deborah together
= 1/4201/73776
= 1 × 73776/4201 = 73776/4201 days
= 17 2359/4201 days = or 17.562 days
Thus, Amanda, Melissa, and Deborah working together will finish the total work (1 work) in 17 2359/4201 days = or 17.562 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 = 48 days
And the number of days required to finish the same work by Melissa = 53 days
And the number of days required to finish the work by Deborah = 58 days
Thus, the number of days required to finish the work by Amanda, Melissa, and Deborah together = ?
Here a = 48 days
And, b = 53 days
And, c = 58 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Amanda, Melissa, and Deborah working together
= 48 × 53 × 58/48 × 53 + 48 × 58 + 53 × 58 days
= 147552/2544 + 2784 + 3074 days
= 147552/8402 days
= 147552/8402 days
= 147552 ÷ 2/8402 ÷ 2 = 73776/4201 days
= 17 2359/4201 days or 17.562
Thus, Amanda, Melissa, and Deborah together will finish the work in 17 2359/4201 days or 17.562 days Answer
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