Question:
Deborah can finish a work in 50 days. Stephanie can finish the same work in 51 days while Rebecca can finish the work in 52 days. How long will it take to finish it if they work together?
Correct Answer
16 3884/3901 days or 16.996 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Deborah = 50 days
And, the number of days required to finish the same work by Stephanie = 51 days
And, the number of days required to finish the same work by Rebecca = 52 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 50 days the work is done by Deborah = 1
∴ The work done by Deborah in 1 day = 1/50
Similarly,
∵ In 51 days the work is done by Stephanie = 1
∴ The work done by Stephanie in 1 day = 1/51
Similarly,
∵ In 52 days the work is done by Rebecca = 1
∴ The work done by Rebecca in 1 day = 1/52 part
Now, the work done by Deborah, Stephanie, and Rebecca together in 1 day
= Deborah's 1 day work + Stephanie's 1 day work + Rebecca's 1 day work
= 1/50 + 1/51 + 1/52
= 1326 + 1300 + 1275/66300
= 3901/66300 part of work
This means in 1 day, 3901/66300 part of work is done by Deborah, Stephanie and Rebecca working together.
Now, the number of days required to finish 3901/66300 part of work by Deborah, Stephanie, and Rebecca working together = 1
∴ the number of days required to finish the whole work (1 work) by Deborah + Stephanie + Rebecca together
= 1/3901/66300
= 1 × 66300/3901 = 66300/3901 days
= 16 3884/3901 days = or 16.996 days
Thus, Deborah, Stephanie, and Rebecca working together will finish the total work (1 work) in 16 3884/3901 days = or 16.996 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 Deborah = 50 days
And the number of days required to finish the same work by Stephanie = 51 days
And the number of days required to finish the work by Rebecca = 52 days
Thus, the number of days required to finish the work by Deborah, Stephanie, and Rebecca together = ?
Here a = 50 days
And, b = 51 days
And, c = 52 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Deborah, Stephanie, and Rebecca working together
= 50 × 51 × 52/50 × 51 + 50 × 52 + 51 × 52 days
= 132600/2550 + 2600 + 2652 days
= 132600/7802 days
= 132600/7802 days
= 132600 ÷ 2/7802 ÷ 2 = 66300/3901 days
= 16 3884/3901 days or 16.996
Thus, Deborah, Stephanie, and Rebecca together will finish the work in 16 3884/3901 days or 16.996 days Answer
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