Question : Christine can finish a work in 90 days. Rachel can finish the same work in 95 days while Carolyn can finish the work in 100 days. How long will it take to finish it if they work together?
Correct Answer 31 329/541 days or 31.608 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Christine = 90 days
And, the number of days required to finish the same work by Rachel = 95 days
And, the number of days required to finish the same work by Carolyn = 100 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 90 days the work is done by Christine = 1
∴ The work done by Christine in 1 day = 1/90
Similarly,
∵ In 95 days the work is done by Rachel = 1
∴ The work done by Rachel in 1 day = 1/95
Similarly,
∵ In 100 days the work is done by Carolyn = 1
∴ The work done by Carolyn in 1 day = 1/100 part
Now, the work done by Christine, Rachel, and Carolyn together in 1 day
= Christine's 1 day work + Rachel's 1 day work + Carolyn's 1 day work
= 1/90 + 1/95 + 1/100
= 190 + 180 + 171/17100
= 541/17100 part of work
This means in 1 day, 541/17100 part of work is done by Christine, Rachel and Carolyn working together.
Now, the number of days required to finish 541/17100 part of work by Christine, Rachel, and Carolyn working together = 1
∴ the number of days required to finish the whole work (1 work) by Christine + Rachel + Carolyn together
= 1/541/17100
= 1 × 17100/541 = 17100/541 days
= 31 329/541 days = or 31.608 days
Thus, Christine, Rachel, and Carolyn working together will finish the total work (1 work) in 31 329/541 days = or 31.608 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 Christine = 90 days
And the number of days required to finish the same work by Rachel = 95 days
And the number of days required to finish the work by Carolyn = 100 days
Thus, the number of days required to finish the work by Christine, Rachel, and Carolyn together = ?
Here a = 90 days
And, b = 95 days
And, c = 100 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Christine, Rachel, and Carolyn working together
= 90 × 95 × 100/90 × 95 + 90 × 100 + 95 × 100 days
= 855000/8550 + 9000 + 9500 days
= 855000/27050 days
= 855000/27050 days
= 855000 ÷ 50/27050 ÷ 50 = 17100/541 days
= 31 329/541 days or 31.608
Thus, Christine, Rachel, and Carolyn together will finish the work in 31 329/541 days or 31.608 days Answer
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