Question : Susan can finish a work in 18 days. Sarah can finish the same work in 23 days while Karen can finish the work in 28 days. How long will it take to finish it if they work together?
Correct Answer 7 329/781 days or 7.421 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Susan = 18 days
And, the number of days required to finish the same work by Sarah = 23 days
And, the number of days required to finish the same work by Karen = 28 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 18 days the work is done by Susan = 1
∴ The work done by Susan in 1 day = 1/18
Similarly,
∵ In 23 days the work is done by Sarah = 1
∴ The work done by Sarah in 1 day = 1/23
Similarly,
∵ In 28 days the work is done by Karen = 1
∴ The work done by Karen in 1 day = 1/28 part
Now, the work done by Susan, Sarah, and Karen together in 1 day
= Susan's 1 day work + Sarah's 1 day work + Karen's 1 day work
= 1/18 + 1/23 + 1/28
= 322 + 252 + 207/5796
= 781/5796 part of work
This means in 1 day, 781/5796 part of work is done by Susan, Sarah and Karen working together.
Now, the number of days required to finish 781/5796 part of work by Susan, Sarah, and Karen working together = 1
∴ the number of days required to finish the whole work (1 work) by Susan + Sarah + Karen together
= 1/781/5796
= 1 × 5796/781 = 5796/781 days
= 7 329/781 days = or 7.421 days
Thus, Susan, Sarah, and Karen working together will finish the total work (1 work) in 7 329/781 days = or 7.421 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 = 18 days
And the number of days required to finish the same work by Sarah = 23 days
And the number of days required to finish the work by Karen = 28 days
Thus, the number of days required to finish the work by Susan, Sarah, and Karen together = ?
Here a = 18 days
And, b = 23 days
And, c = 28 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Susan, Sarah, and Karen working together
= 18 × 23 × 28/18 × 23 + 18 × 28 + 23 × 28 days
= 11592/414 + 504 + 644 days
= 11592/1562 days
= 11592/1562 days
= 11592 ÷ 2/1562 ÷ 2 = 5796/781 days
= 7 329/781 days or 7.421
Thus, Susan, Sarah, and Karen together will finish the work in 7 329/781 days or 7.421 days Answer
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