Question : Nicole can finish a work in 82 days. Samantha can finish the same work in 87 days while Katherine can finish the work in 92 days. How long will it take to finish it if they work together?
Correct Answer 28 10616/11341 days or 28.936 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Nicole = 82 days
And, the number of days required to finish the same work by Samantha = 87 days
And, the number of days required to finish the same work by Katherine = 92 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 82 days the work is done by Nicole = 1
∴ The work done by Nicole in 1 day = 1/82
Similarly,
∵ In 87 days the work is done by Samantha = 1
∴ The work done by Samantha in 1 day = 1/87
Similarly,
∵ In 92 days the work is done by Katherine = 1
∴ The work done by Katherine in 1 day = 1/92 part
Now, the work done by Nicole, Samantha, and Katherine together in 1 day
= Nicole's 1 day work + Samantha's 1 day work + Katherine's 1 day work
= 1/82 + 1/87 + 1/92
= 4002 + 3772 + 3567/328164
= 11341/328164 part of work
This means in 1 day, 11341/328164 part of work is done by Nicole, Samantha and Katherine working together.
Now, the number of days required to finish 11341/328164 part of work by Nicole, Samantha, and Katherine working together = 1
∴ the number of days required to finish the whole work (1 work) by Nicole + Samantha + Katherine together
= 1/11341/328164
= 1 × 328164/11341 = 328164/11341 days
= 28 10616/11341 days = or 28.936 days
Thus, Nicole, Samantha, and Katherine working together will finish the total work (1 work) in 28 10616/11341 days = or 28.936 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 Nicole = 82 days
And the number of days required to finish the same work by Samantha = 87 days
And the number of days required to finish the work by Katherine = 92 days
Thus, the number of days required to finish the work by Nicole, Samantha, and Katherine together = ?
Here a = 82 days
And, b = 87 days
And, c = 92 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Nicole, Samantha, and Katherine working together
= 82 × 87 × 92/82 × 87 + 82 × 92 + 87 × 92 days
= 656328/7134 + 7544 + 8004 days
= 656328/22682 days
= 656328/22682 days
= 656328 ÷ 2/22682 ÷ 2 = 328164/11341 days
= 28 10616/11341 days or 28.936
Thus, Nicole, Samantha, and Katherine together will finish the work in 28 10616/11341 days or 28.936 days Answer
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