Question : Emma can finish a work in 80 days. Helen can finish the same work in 85 days while Samantha can finish the work in 90 days. How long will it take to finish it if they work together?
Correct Answer 28 116/433 days or 28.268 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Emma = 80 days
And, the number of days required to finish the same work by Helen = 85 days
And, the number of days required to finish the same work by Samantha = 90 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 80 days the work is done by Emma = 1
∴ The work done by Emma in 1 day = 1/80
Similarly,
∵ In 85 days the work is done by Helen = 1
∴ The work done by Helen in 1 day = 1/85
Similarly,
∵ In 90 days the work is done by Samantha = 1
∴ The work done by Samantha in 1 day = 1/90 part
Now, the work done by Emma, Helen, and Samantha together in 1 day
= Emma's 1 day work + Helen's 1 day work + Samantha's 1 day work
= 1/80 + 1/85 + 1/90
= 153 + 144 + 136/12240
= 433/12240 part of work
This means in 1 day, 433/12240 part of work is done by Emma, Helen and Samantha working together.
Now, the number of days required to finish 433/12240 part of work by Emma, Helen, and Samantha working together = 1
∴ the number of days required to finish the whole work (1 work) by Emma + Helen + Samantha together
= 1/433/12240
= 1 × 12240/433 = 12240/433 days
= 28 116/433 days = or 28.268 days
Thus, Emma, Helen, and Samantha working together will finish the total work (1 work) in 28 116/433 days = or 28.268 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 Emma = 80 days
And the number of days required to finish the same work by Helen = 85 days
And the number of days required to finish the work by Samantha = 90 days
Thus, the number of days required to finish the work by Emma, Helen, and Samantha together = ?
Here a = 80 days
And, b = 85 days
And, c = 90 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Emma, Helen, and Samantha working together
= 80 × 85 × 90/80 × 85 + 80 × 90 + 85 × 90 days
= 612000/6800 + 7200 + 7650 days
= 612000/21650 days
= 612000/21650 days
= 612000 ÷ 50/21650 ÷ 50 = 12240/433 days
= 28 116/433 days or 28.268
Thus, Emma, Helen, and Samantha together will finish the work in 28 116/433 days or 28.268 days Answer
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