Question : Melissa can finish a work in 52 days. Stephanie can finish the same work in 57 days while Rebecca can finish the work in 62 days. How long will it take to finish it if they work together?
Correct Answer 18 4386/4861 days or 18.902 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Melissa = 52 days
And, the number of days required to finish the same work by Stephanie = 57 days
And, the number of days required to finish the same work by Rebecca = 62 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 52 days the work is done by Melissa = 1
∴ The work done by Melissa in 1 day = 1/52
Similarly,
∵ In 57 days the work is done by Stephanie = 1
∴ The work done by Stephanie in 1 day = 1/57
Similarly,
∵ In 62 days the work is done by Rebecca = 1
∴ The work done by Rebecca in 1 day = 1/62 part
Now, the work done by Melissa, Stephanie, and Rebecca together in 1 day
= Melissa's 1 day work + Stephanie's 1 day work + Rebecca's 1 day work
= 1/52 + 1/57 + 1/62
= 1767 + 1612 + 1482/91884
= 4861/91884 part of work
This means in 1 day, 4861/91884 part of work is done by Melissa, Stephanie and Rebecca working together.
Now, the number of days required to finish 4861/91884 part of work by Melissa, Stephanie, and Rebecca working together = 1
∴ the number of days required to finish the whole work (1 work) by Melissa + Stephanie + Rebecca together
= 1/4861/91884
= 1 × 91884/4861 = 91884/4861 days
= 18 4386/4861 days = or 18.902 days
Thus, Melissa, Stephanie, and Rebecca working together will finish the total work (1 work) in 18 4386/4861 days = or 18.902 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 = 52 days
And the number of days required to finish the same work by Stephanie = 57 days
And the number of days required to finish the work by Rebecca = 62 days
Thus, the number of days required to finish the work by Melissa, Stephanie, and Rebecca together = ?
Here a = 52 days
And, b = 57 days
And, c = 62 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Melissa, Stephanie, and Rebecca working together
= 52 × 57 × 62/52 × 57 + 52 × 62 + 57 × 62 days
= 183768/2964 + 3224 + 3534 days
= 183768/9722 days
= 183768/9722 days
= 183768 ÷ 2/9722 ÷ 2 = 91884/4861 days
= 18 4386/4861 days or 18.902
Thus, Melissa, Stephanie, and Rebecca together will finish the work in 18 4386/4861 days or 18.902 days Answer
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