Question:
Susan can finish a work in 14 days. Jessica can finish the same work in 15 days while Sarah can finish the work in 16 days. How long will it take to finish it if they work together?
Correct Answer
4 332/337 days or 4.985 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Susan = 14 days
And, the number of days required to finish the same work by Jessica = 15 days
And, the number of days required to finish the same work by Sarah = 16 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 14 days the work is done by Susan = 1
∴ The work done by Susan in 1 day = 1/14
Similarly,
∵ In 15 days the work is done by Jessica = 1
∴ The work done by Jessica in 1 day = 1/15
Similarly,
∵ In 16 days the work is done by Sarah = 1
∴ The work done by Sarah in 1 day = 1/16 part
Now, the work done by Susan, Jessica, and Sarah together in 1 day
= Susan's 1 day work + Jessica's 1 day work + Sarah's 1 day work
= 1/14 + 1/15 + 1/16
= 120 + 112 + 105/1680
= 337/1680 part of work
This means in 1 day, 337/1680 part of work is done by Susan, Jessica and Sarah working together.
Now, the number of days required to finish 337/1680 part of work by Susan, Jessica, and Sarah working together = 1
∴ the number of days required to finish the whole work (1 work) by Susan + Jessica + Sarah together
= 1/337/1680
= 1 × 1680/337 = 1680/337 days
= 4 332/337 days = or 4.985 days
Thus, Susan, Jessica, and Sarah working together will finish the total work (1 work) in 4 332/337 days = or 4.985 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 Susan = 14 days
And the number of days required to finish the same work by Jessica = 15 days
And the number of days required to finish the work by Sarah = 16 days
Thus, the number of days required to finish the work by Susan, Jessica, and Sarah together = ?
Here a = 14 days
And, b = 15 days
And, c = 16 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Susan, Jessica, and Sarah working together
= 14 × 15 × 16/14 × 15 + 14 × 16 + 15 × 16 days
= 3360/210 + 224 + 240 days
= 3360/674 days
= 3360/674 days
= 3360 ÷ 2/674 ÷ 2 = 1680/337 days
= 4 332/337 days or 4.985
Thus, Susan, Jessica, and Sarah together will finish the work in 4 332/337 days or 4.985 days Answer
Similar Questions
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