Question : Pamela can finish a work in 78 days. Nicole can finish the same work in 83 days while Helen can finish the work in 88 days. How long will it take to finish it if they work together?
Correct Answer 27 6189/10321 days or 27.6 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Pamela = 78 days
And, the number of days required to finish the same work by Nicole = 83 days
And, the number of days required to finish the same work by Helen = 88 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 78 days the work is done by Pamela = 1
∴ The work done by Pamela in 1 day = 1/78
Similarly,
∵ In 83 days the work is done by Nicole = 1
∴ The work done by Nicole in 1 day = 1/83
Similarly,
∵ In 88 days the work is done by Helen = 1
∴ The work done by Helen in 1 day = 1/88 part
Now, the work done by Pamela, Nicole, and Helen together in 1 day
= Pamela's 1 day work + Nicole's 1 day work + Helen's 1 day work
= 1/78 + 1/83 + 1/88
= 3652 + 3432 + 3237/284856
= 10321/284856 part of work
This means in 1 day, 10321/284856 part of work is done by Pamela, Nicole and Helen working together.
Now, the number of days required to finish 10321/284856 part of work by Pamela, Nicole, and Helen working together = 1
∴ the number of days required to finish the whole work (1 work) by Pamela + Nicole + Helen together
= 1/10321/284856
= 1 × 284856/10321 = 284856/10321 days
= 27 6189/10321 days = or 27.6 days
Thus, Pamela, Nicole, and Helen working together will finish the total work (1 work) in 27 6189/10321 days = or 27.6 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 Pamela = 78 days
And the number of days required to finish the same work by Nicole = 83 days
And the number of days required to finish the work by Helen = 88 days
Thus, the number of days required to finish the work by Pamela, Nicole, and Helen together = ?
Here a = 78 days
And, b = 83 days
And, c = 88 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Pamela, Nicole, and Helen working together
= 78 × 83 × 88/78 × 83 + 78 × 88 + 83 × 88 days
= 569712/6474 + 6864 + 7304 days
= 569712/20642 days
= 569712/20642 days
= 569712 ÷ 2/20642 ÷ 2 = 284856/10321 days
= 27 6189/10321 days or 27.6
Thus, Pamela, Nicole, and Helen together will finish the work in 27 6189/10321 days or 27.6 days Answer
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