Question:
Emily can finish a work in 36 days. Donna can finish the same work in 37 days while Michelle can finish the work in 38 days. How long will it take to finish it if they work together?
Correct Answer
12 672/2053 days or 12.327 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Emily = 36 days
And, the number of days required to finish the same work by Donna = 37 days
And, the number of days required to finish the same work by Michelle = 38 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 36 days the work is done by Emily = 1
∴ The work done by Emily in 1 day = 1/36
Similarly,
∵ In 37 days the work is done by Donna = 1
∴ The work done by Donna in 1 day = 1/37
Similarly,
∵ In 38 days the work is done by Michelle = 1
∴ The work done by Michelle in 1 day = 1/38 part
Now, the work done by Emily, Donna, and Michelle together in 1 day
= Emily's 1 day work + Donna's 1 day work + Michelle's 1 day work
= 1/36 + 1/37 + 1/38
= 703 + 684 + 666/25308
= 2053/25308 part of work
This means in 1 day, 2053/25308 part of work is done by Emily, Donna and Michelle working together.
Now, the number of days required to finish 2053/25308 part of work by Emily, Donna, and Michelle working together = 1
∴ the number of days required to finish the whole work (1 work) by Emily + Donna + Michelle together
= 1/2053/25308
= 1 × 25308/2053 = 25308/2053 days
= 12 672/2053 days = or 12.327 days
Thus, Emily, Donna, and Michelle working together will finish the total work (1 work) in 12 672/2053 days = or 12.327 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 Emily = 36 days
And the number of days required to finish the same work by Donna = 37 days
And the number of days required to finish the work by Michelle = 38 days
Thus, the number of days required to finish the work by Emily, Donna, and Michelle together = ?
Here a = 36 days
And, b = 37 days
And, c = 38 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Emily, Donna, and Michelle working together
= 36 × 37 × 38/36 × 37 + 36 × 38 + 37 × 38 days
= 50616/1332 + 1368 + 1406 days
= 50616/4106 days
= 50616/4106 days
= 50616 ÷ 2/4106 ÷ 2 = 25308/2053 days
= 12 672/2053 days or 12.327
Thus, Emily, Donna, and Michelle together will finish the work in 12 672/2053 days or 12.327 days Answer
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