Question : Jessica can finish a work in 16 days. Sarah can finish the same work in 17 days while Karen can finish the work in 18 days. How long will it take to finish it if they work together?
Correct Answer 5 283/433 days or 5.654 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Jessica = 16 days
And, the number of days required to finish the same work by Sarah = 17 days
And, the number of days required to finish the same work by Karen = 18 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 Jessica = 1
∴ The work done by Jessica in 1 day = 1/16
Similarly,
∵ In 17 days the work is done by Sarah = 1
∴ The work done by Sarah in 1 day = 1/17
Similarly,
∵ In 18 days the work is done by Karen = 1
∴ The work done by Karen in 1 day = 1/18 part
Now, the work done by Jessica, Sarah, and Karen together in 1 day
= Jessica's 1 day work + Sarah's 1 day work + Karen's 1 day work
= 1/16 + 1/17 + 1/18
= 153 + 144 + 136/2448
= 433/2448 part of work
This means in 1 day, 433/2448 part of work is done by Jessica, Sarah and Karen working together.
Now, the number of days required to finish 433/2448 part of work by Jessica, Sarah, and Karen working together = 1
∴ the number of days required to finish the whole work (1 work) by Jessica + Sarah + Karen together
= 1/433/2448
= 1 × 2448/433 = 2448/433 days
= 5 283/433 days = or 5.654 days
Thus, Jessica, Sarah, and Karen working together will finish the total work (1 work) in 5 283/433 days = or 5.654 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 Jessica = 16 days
And the number of days required to finish the same work by Sarah = 17 days
And the number of days required to finish the work by Karen = 18 days
Thus, the number of days required to finish the work by Jessica, Sarah, and Karen together = ?
Here a = 16 days
And, b = 17 days
And, c = 18 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jessica, Sarah, and Karen working together
= 16 × 17 × 18/16 × 17 + 16 × 18 + 17 × 18 days
= 4896/272 + 288 + 306 days
= 4896/866 days
= 4896/866 days
= 4896 ÷ 2/866 ÷ 2 = 2448/433 days
= 5 283/433 days or 5.654
Thus, Jessica, Sarah, and Karen together will finish the work in 5 283/433 days or 5.654 days Answer
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