Question:
Carol can finish a work in 46 days. Dorothy can finish the same work in 51 days while Melissa can finish the work in 56 days. How long will it take to finish it if they work together?
Correct Answer
16 3464/3889 days or 16.891 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Carol = 46 days
And, the number of days required to finish the same work by Dorothy = 51 days
And, the number of days required to finish the same work by Melissa = 56 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 Carol = 1
∴ The work done by Carol in 1 day = 1/46
Similarly,
∵ In 51 days the work is done by Dorothy = 1
∴ The work done by Dorothy in 1 day = 1/51
Similarly,
∵ In 56 days the work is done by Melissa = 1
∴ The work done by Melissa in 1 day = 1/56 part
Now, the work done by Carol, Dorothy, and Melissa together in 1 day
= Carol's 1 day work + Dorothy's 1 day work + Melissa's 1 day work
= 1/46 + 1/51 + 1/56
= 1428 + 1288 + 1173/65688
= 3889/65688 part of work
This means in 1 day, 3889/65688 part of work is done by Carol, Dorothy and Melissa working together.
Now, the number of days required to finish 3889/65688 part of work by Carol, Dorothy, and Melissa working together = 1
∴ the number of days required to finish the whole work (1 work) by Carol + Dorothy + Melissa together
= 1/3889/65688
= 1 × 65688/3889 = 65688/3889 days
= 16 3464/3889 days = or 16.891 days
Thus, Carol, Dorothy, and Melissa working together will finish the total work (1 work) in 16 3464/3889 days = or 16.891 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 Carol = 46 days
And the number of days required to finish the same work by Dorothy = 51 days
And the number of days required to finish the work by Melissa = 56 days
Thus, the number of days required to finish the work by Carol, Dorothy, and Melissa together = ?
Here a = 46 days
And, b = 51 days
And, c = 56 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Carol, Dorothy, and Melissa working together
= 46 × 51 × 56/46 × 51 + 46 × 56 + 51 × 56 days
= 131376/2346 + 2576 + 2856 days
= 131376/7778 days
= 131376/7778 days
= 131376 ÷ 2/7778 ÷ 2 = 65688/3889 days
= 16 3464/3889 days or 16.891
Thus, Carol, Dorothy, and Melissa together will finish the work in 16 3464/3889 days or 16.891 days Answer
Similar Questions
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