Question : Jacob can finish a work in 65 days. Nicholas can finish the same work in 70 days while Eric can finish the work in 75 days. How long will it take to finish it if they work together?
Correct Answer 23 149/587 days or 23.254 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Jacob = 65 days
And, the number of days required to finish the same work by Nicholas = 70 days
And, the number of days required to finish the same work by Eric = 75 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 65 days the work is done by Jacob = 1
∴ The work done by Jacob in 1 day = 1/65
Similarly,
∵ In 70 days the work is done by Nicholas = 1
∴ The work done by Nicholas in 1 day = 1/70
Similarly,
∵ In 75 days the work is done by Eric = 1
∴ The work done by Eric in 1 day = 1/75 part
Now, the work done by Jacob, Nicholas, and Eric together in 1 day
= Jacob's 1 day work + Nicholas's 1 day work + Eric's 1 day work
= 1/65 + 1/70 + 1/75
= 210 + 195 + 182/13650
= 587/13650 part of work
This means in 1 day, 587/13650 part of work is done by Jacob, Nicholas and Eric working together.
Now, the number of days required to finish 587/13650 part of work by Jacob, Nicholas, and Eric working together = 1
∴ the number of days required to finish the whole work (1 work) by Jacob + Nicholas + Eric together
= 1/587/13650
= 1 × 13650/587 = 13650/587 days
= 23 149/587 days = or 23.254 days
Thus, Jacob, Nicholas, and Eric working together will finish the total work (1 work) in 23 149/587 days = or 23.254 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 Jacob = 65 days
And the number of days required to finish the same work by Nicholas = 70 days
And the number of days required to finish the work by Eric = 75 days
Thus, the number of days required to finish the work by Jacob, Nicholas, and Eric together = ?
Here a = 65 days
And, b = 70 days
And, c = 75 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jacob, Nicholas, and Eric working together
= 65 × 70 × 75/65 × 70 + 65 × 75 + 70 × 75 days
= 341250/4550 + 4875 + 5250 days
= 341250/14675 days
= 341250/14675 days
= 341250 ÷ 25/14675 ÷ 25 = 13650/587 days
= 23 149/587 days or 23.254
Thus, Jacob, Nicholas, and Eric together will finish the work in 23 149/587 days or 23.254 days Answer
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