Question : Melissa can finish a work in 48 days. Deborah can finish the same work in 49 days while Stephanie can finish the work in 50 days. How long will it take to finish it if they work together?
Correct Answer 16 1184/3601 days or 16.329 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Melissa = 48 days
And, the number of days required to finish the same work by Deborah = 49 days
And, the number of days required to finish the same work by Stephanie = 50 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 48 days the work is done by Melissa = 1
∴ The work done by Melissa in 1 day = 1/48
Similarly,
∵ In 49 days the work is done by Deborah = 1
∴ The work done by Deborah in 1 day = 1/49
Similarly,
∵ In 50 days the work is done by Stephanie = 1
∴ The work done by Stephanie in 1 day = 1/50 part
Now, the work done by Melissa, Deborah, and Stephanie together in 1 day
= Melissa's 1 day work + Deborah's 1 day work + Stephanie's 1 day work
= 1/48 + 1/49 + 1/50
= 1225 + 1200 + 1176/58800
= 3601/58800 part of work
This means in 1 day, 3601/58800 part of work is done by Melissa, Deborah and Stephanie working together.
Now, the number of days required to finish 3601/58800 part of work by Melissa, Deborah, and Stephanie working together = 1
∴ the number of days required to finish the whole work (1 work) by Melissa + Deborah + Stephanie together
= 1/3601/58800
= 1 × 58800/3601 = 58800/3601 days
= 16 1184/3601 days = or 16.329 days
Thus, Melissa, Deborah, and Stephanie working together will finish the total work (1 work) in 16 1184/3601 days = or 16.329 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 Melissa = 48 days
And the number of days required to finish the same work by Deborah = 49 days
And the number of days required to finish the work by Stephanie = 50 days
Thus, the number of days required to finish the work by Melissa, Deborah, and Stephanie together = ?
Here a = 48 days
And, b = 49 days
And, c = 50 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Melissa, Deborah, and Stephanie working together
= 48 × 49 × 50/48 × 49 + 48 × 50 + 49 × 50 days
= 117600/2352 + 2400 + 2450 days
= 117600/7202 days
= 117600/7202 days
= 117600 ÷ 2/7202 ÷ 2 = 58800/3601 days
= 16 1184/3601 days or 16.329
Thus, Melissa, Deborah, and Stephanie together will finish the work in 16 1184/3601 days or 16.329 days Answer
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