Question:
Dorothy can finish a work in 50 days. Deborah can finish the same work in 55 days while Stephanie can finish the work in 60 days. How long will it take to finish it if they work together?
Correct Answer
18 42/181 days or 18.232 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Dorothy = 50 days
And, the number of days required to finish the same work by Deborah = 55 days
And, the number of days required to finish the same work by Stephanie = 60 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 Dorothy = 1
∴ The work done by Dorothy in 1 day = 1/50
Similarly,
∵ In 55 days the work is done by Deborah = 1
∴ The work done by Deborah in 1 day = 1/55
Similarly,
∵ In 60 days the work is done by Stephanie = 1
∴ The work done by Stephanie in 1 day = 1/60 part
Now, the work done by Dorothy, Deborah, and Stephanie together in 1 day
= Dorothy's 1 day work + Deborah's 1 day work + Stephanie's 1 day work
= 1/50 + 1/55 + 1/60
= 66 + 60 + 55/3300
= 181/3300 part of work
This means in 1 day, 181/3300 part of work is done by Dorothy, Deborah and Stephanie working together.
Now, the number of days required to finish 181/3300 part of work by Dorothy, Deborah, and Stephanie working together = 1
∴ the number of days required to finish the whole work (1 work) by Dorothy + Deborah + Stephanie together
= 1/181/3300
= 1 × 3300/181 = 3300/181 days
= 18 42/181 days = or 18.232 days
Thus, Dorothy, Deborah, and Stephanie working together will finish the total work (1 work) in 18 42/181 days = or 18.232 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 Dorothy = 50 days
And the number of days required to finish the same work by Deborah = 55 days
And the number of days required to finish the work by Stephanie = 60 days
Thus, the number of days required to finish the work by Dorothy, Deborah, and Stephanie together = ?
Here a = 50 days
And, b = 55 days
And, c = 60 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Dorothy, Deborah, and Stephanie working together
= 50 × 55 × 60/50 × 55 + 50 × 60 + 55 × 60 days
= 165000/2750 + 3000 + 3300 days
= 165000/9050 days
= 165000/9050 days
= 165000 ÷ 50/9050 ÷ 50 = 3300/181 days
= 18 42/181 days or 18.232
Thus, Dorothy, Deborah, and Stephanie together will finish the work in 18 42/181 days or 18.232 days Answer
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