Question : Dorothy can finish a work in 46 days. Melissa can finish the same work in 47 days while Deborah can finish the work in 48 days. How long will it take to finish it if they work together?
Correct Answer 15 2193/3313 days or 15.662 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Dorothy = 46 days
And, the number of days required to finish the same work by Melissa = 47 days
And, the number of days required to finish the same work by Deborah = 48 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 46 days the work is done by Dorothy = 1
∴ The work done by Dorothy in 1 day = 1/46
Similarly,
∵ In 47 days the work is done by Melissa = 1
∴ The work done by Melissa in 1 day = 1/47
Similarly,
∵ In 48 days the work is done by Deborah = 1
∴ The work done by Deborah in 1 day = 1/48 part
Now, the work done by Dorothy, Melissa, and Deborah together in 1 day
= Dorothy's 1 day work + Melissa's 1 day work + Deborah's 1 day work
= 1/46 + 1/47 + 1/48
= 1128 + 1104 + 1081/51888
= 3313/51888 part of work
This means in 1 day, 3313/51888 part of work is done by Dorothy, Melissa and Deborah working together.
Now, the number of days required to finish 3313/51888 part of work by Dorothy, Melissa, and Deborah working together = 1
∴ the number of days required to finish the whole work (1 work) by Dorothy + Melissa + Deborah together
= 1/3313/51888
= 1 × 51888/3313 = 51888/3313 days
= 15 2193/3313 days = or 15.662 days
Thus, Dorothy, Melissa, and Deborah working together will finish the total work (1 work) in 15 2193/3313 days = or 15.662 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 = 46 days
And the number of days required to finish the same work by Melissa = 47 days
And the number of days required to finish the work by Deborah = 48 days
Thus, the number of days required to finish the work by Dorothy, Melissa, and Deborah together = ?
Here a = 46 days
And, b = 47 days
And, c = 48 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Dorothy, Melissa, and Deborah working together
= 46 × 47 × 48/46 × 47 + 46 × 48 + 47 × 48 days
= 103776/2162 + 2208 + 2256 days
= 103776/6626 days
= 103776/6626 days
= 103776 ÷ 2/6626 ÷ 2 = 51888/3313 days
= 15 2193/3313 days or 15.662
Thus, Dorothy, Melissa, and Deborah together will finish the work in 15 2193/3313 days or 15.662 days Answer
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