Question:
Margaret can finish a work in 32 days. Ashley can finish the same work in 37 days while Kimberly can finish the work in 42 days. How long will it take to finish it if they work together?
Correct Answer
12 372/2041 days or 12.182 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Margaret = 32 days
And, the number of days required to finish the same work by Ashley = 37 days
And, the number of days required to finish the same work by Kimberly = 42 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 32 days the work is done by Margaret = 1
∴ The work done by Margaret in 1 day = 1/32
Similarly,
∵ In 37 days the work is done by Ashley = 1
∴ The work done by Ashley in 1 day = 1/37
Similarly,
∵ In 42 days the work is done by Kimberly = 1
∴ The work done by Kimberly in 1 day = 1/42 part
Now, the work done by Margaret, Ashley, and Kimberly together in 1 day
= Margaret's 1 day work + Ashley's 1 day work + Kimberly's 1 day work
= 1/32 + 1/37 + 1/42
= 777 + 672 + 592/24864
= 2041/24864 part of work
This means in 1 day, 2041/24864 part of work is done by Margaret, Ashley and Kimberly working together.
Now, the number of days required to finish 2041/24864 part of work by Margaret, Ashley, and Kimberly working together = 1
∴ the number of days required to finish the whole work (1 work) by Margaret + Ashley + Kimberly together
= 1/2041/24864
= 1 × 24864/2041 = 24864/2041 days
= 12 372/2041 days = or 12.182 days
Thus, Margaret, Ashley, and Kimberly working together will finish the total work (1 work) in 12 372/2041 days = or 12.182 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 Margaret = 32 days
And the number of days required to finish the same work by Ashley = 37 days
And the number of days required to finish the work by Kimberly = 42 days
Thus, the number of days required to finish the work by Margaret, Ashley, and Kimberly together = ?
Here a = 32 days
And, b = 37 days
And, c = 42 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Margaret, Ashley, and Kimberly working together
= 32 × 37 × 42/32 × 37 + 32 × 42 + 37 × 42 days
= 49728/1184 + 1344 + 1554 days
= 49728/4082 days
= 49728/4082 days
= 49728 ÷ 2/4082 ÷ 2 = 24864/2041 days
= 12 372/2041 days or 12.182
Thus, Margaret, Ashley, and Kimberly together will finish the work in 12 372/2041 days or 12.182 days Answer
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