Question : Eric can finish a work in 71 days. Stephen can finish the same work in 76 days while Larry can finish the work in 81 days. How long will it take to finish it if they work together?
Correct Answer 25 4501/17303 days or 25.26 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Eric = 71 days
And, the number of days required to finish the same work by Stephen = 76 days
And, the number of days required to finish the same work by Larry = 81 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 71 days the work is done by Eric = 1
∴ The work done by Eric in 1 day = 1/71
Similarly,
∵ In 76 days the work is done by Stephen = 1
∴ The work done by Stephen in 1 day = 1/76
Similarly,
∵ In 81 days the work is done by Larry = 1
∴ The work done by Larry in 1 day = 1/81 part
Now, the work done by Eric, Stephen, and Larry together in 1 day
= Eric's 1 day work + Stephen's 1 day work + Larry's 1 day work
= 1/71 + 1/76 + 1/81
= 6156 + 5751 + 5396/437076
= 17303/437076 part of work
This means in 1 day, 17303/437076 part of work is done by Eric, Stephen and Larry working together.
Now, the number of days required to finish 17303/437076 part of work by Eric, Stephen, and Larry working together = 1
∴ the number of days required to finish the whole work (1 work) by Eric + Stephen + Larry together
= 1/17303/437076
= 1 × 437076/17303 = 437076/17303 days
= 25 4501/17303 days = or 25.26 days
Thus, Eric, Stephen, and Larry working together will finish the total work (1 work) in 25 4501/17303 days = or 25.26 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 Eric = 71 days
And the number of days required to finish the same work by Stephen = 76 days
And the number of days required to finish the work by Larry = 81 days
Thus, the number of days required to finish the work by Eric, Stephen, and Larry together = ?
Here a = 71 days
And, b = 76 days
And, c = 81 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Eric, Stephen, and Larry working together
= 71 × 76 × 81/71 × 76 + 71 × 81 + 76 × 81 days
= 437076/5396 + 5751 + 6156 days
= 437076/17303 days
= 437076/17303 days
= 25 4501/17303 days or 25.26
Thus, Eric, Stephen, and Larry together will finish the work in 25 4501/17303 days or 25.26 days Answer
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