Question : Steven can finish a work in 37 days. Andrew can finish the same work in 42 days while Joshua can finish the work in 47 days. How long will it take to finish it if they work together?
Correct Answer 13 4567/5267 days or 13.867 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Steven = 37 days
And, the number of days required to finish the same work by Andrew = 42 days
And, the number of days required to finish the same work by Joshua = 47 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 37 days the work is done by Steven = 1
∴ The work done by Steven in 1 day = 1/37
Similarly,
∵ In 42 days the work is done by Andrew = 1
∴ The work done by Andrew in 1 day = 1/42
Similarly,
∵ In 47 days the work is done by Joshua = 1
∴ The work done by Joshua in 1 day = 1/47 part
Now, the work done by Steven, Andrew, and Joshua together in 1 day
= Steven's 1 day work + Andrew's 1 day work + Joshua's 1 day work
= 1/37 + 1/42 + 1/47
= 1974 + 1739 + 1554/73038
= 5267/73038 part of work
This means in 1 day, 5267/73038 part of work is done by Steven, Andrew and Joshua working together.
Now, the number of days required to finish 5267/73038 part of work by Steven, Andrew, and Joshua working together = 1
∴ the number of days required to finish the whole work (1 work) by Steven + Andrew + Joshua together
= 1/5267/73038
= 1 × 73038/5267 = 73038/5267 days
= 13 4567/5267 days = or 13.867 days
Thus, Steven, Andrew, and Joshua working together will finish the total work (1 work) in 13 4567/5267 days = or 13.867 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 Steven = 37 days
And the number of days required to finish the same work by Andrew = 42 days
And the number of days required to finish the work by Joshua = 47 days
Thus, the number of days required to finish the work by Steven, Andrew, and Joshua together = ?
Here a = 37 days
And, b = 42 days
And, c = 47 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Steven, Andrew, and Joshua working together
= 37 × 42 × 47/37 × 42 + 37 × 47 + 42 × 47 days
= 73038/1554 + 1739 + 1974 days
= 73038/5267 days
= 73038/5267 days
= 13 4567/5267 days or 13.867
Thus, Steven, Andrew, and Joshua together will finish the work in 13 4567/5267 days or 13.867 days Answer
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