Question:
Sandra can finish a work in 30 days. Ashley can finish the same work in 31 days while Kimberly can finish the work in 32 days. How long will it take to finish it if they work together?
Correct Answer
10 470/1441 days or 10.326 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Sandra = 30 days
And, the number of days required to finish the same work by Ashley = 31 days
And, the number of days required to finish the same work by Kimberly = 32 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 30 days the work is done by Sandra = 1
∴ The work done by Sandra in 1 day = 1/30
Similarly,
∵ In 31 days the work is done by Ashley = 1
∴ The work done by Ashley in 1 day = 1/31
Similarly,
∵ In 32 days the work is done by Kimberly = 1
∴ The work done by Kimberly in 1 day = 1/32 part
Now, the work done by Sandra, Ashley, and Kimberly together in 1 day
= Sandra's 1 day work + Ashley's 1 day work + Kimberly's 1 day work
= 1/30 + 1/31 + 1/32
= 496 + 480 + 465/14880
= 1441/14880 part of work
This means in 1 day, 1441/14880 part of work is done by Sandra, Ashley and Kimberly working together.
Now, the number of days required to finish 1441/14880 part of work by Sandra, Ashley, and Kimberly working together = 1
∴ the number of days required to finish the whole work (1 work) by Sandra + Ashley + Kimberly together
= 1/1441/14880
= 1 × 14880/1441 = 14880/1441 days
= 10 470/1441 days = or 10.326 days
Thus, Sandra, Ashley, and Kimberly working together will finish the total work (1 work) in 10 470/1441 days = or 10.326 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 Sandra = 30 days
And the number of days required to finish the same work by Ashley = 31 days
And the number of days required to finish the work by Kimberly = 32 days
Thus, the number of days required to finish the work by Sandra, Ashley, and Kimberly together = ?
Here a = 30 days
And, b = 31 days
And, c = 32 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Sandra, Ashley, and Kimberly working together
= 30 × 31 × 32/30 × 31 + 30 × 32 + 31 × 32 days
= 29760/930 + 960 + 992 days
= 29760/2882 days
= 29760/2882 days
= 29760 ÷ 2/2882 ÷ 2 = 14880/1441 days
= 10 470/1441 days or 10.326
Thus, Sandra, Ashley, and Kimberly together will finish the work in 10 470/1441 days or 10.326 days Answer
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