Question : Barbara can finish a work in 16 days. Jessica can finish the same work in 21 days while Sarah can finish the work in 26 days. How long will it take to finish it if they work together?
Correct Answer 6 474/649 days or 6.73 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Barbara = 16 days
And, the number of days required to finish the same work by Jessica = 21 days
And, the number of days required to finish the same work by Sarah = 26 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 16 days the work is done by Barbara = 1
∴ The work done by Barbara in 1 day = 1/16
Similarly,
∵ In 21 days the work is done by Jessica = 1
∴ The work done by Jessica in 1 day = 1/21
Similarly,
∵ In 26 days the work is done by Sarah = 1
∴ The work done by Sarah in 1 day = 1/26 part
Now, the work done by Barbara, Jessica, and Sarah together in 1 day
= Barbara's 1 day work + Jessica's 1 day work + Sarah's 1 day work
= 1/16 + 1/21 + 1/26
= 273 + 208 + 168/4368
= 649/4368 part of work
This means in 1 day, 649/4368 part of work is done by Barbara, Jessica and Sarah working together.
Now, the number of days required to finish 649/4368 part of work by Barbara, Jessica, and Sarah working together = 1
∴ the number of days required to finish the whole work (1 work) by Barbara + Jessica + Sarah together
= 1/649/4368
= 1 × 4368/649 = 4368/649 days
= 6 474/649 days = or 6.73 days
Thus, Barbara, Jessica, and Sarah working together will finish the total work (1 work) in 6 474/649 days = or 6.73 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 Barbara = 16 days
And the number of days required to finish the same work by Jessica = 21 days
And the number of days required to finish the work by Sarah = 26 days
Thus, the number of days required to finish the work by Barbara, Jessica, and Sarah together = ?
Here a = 16 days
And, b = 21 days
And, c = 26 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Barbara, Jessica, and Sarah working together
= 16 × 21 × 26/16 × 21 + 16 × 26 + 21 × 26 days
= 8736/336 + 416 + 546 days
= 8736/1298 days
= 8736/1298 days
= 8736 ÷ 2/1298 ÷ 2 = 4368/649 days
= 6 474/649 days or 6.73
Thus, Barbara, Jessica, and Sarah together will finish the work in 6 474/649 days or 6.73 days Answer
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