Question : Larry can finish a work in 77 days. Scott can finish the same work in 82 days while Brandon can finish the work in 87 days. How long will it take to finish it if they work together?
Correct Answer 27 5349/20147 days or 27.265 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Larry = 77 days
And, the number of days required to finish the same work by Scott = 82 days
And, the number of days required to finish the same work by Brandon = 87 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 77 days the work is done by Larry = 1
∴ The work done by Larry in 1 day = 1/77
Similarly,
∵ In 82 days the work is done by Scott = 1
∴ The work done by Scott in 1 day = 1/82
Similarly,
∵ In 87 days the work is done by Brandon = 1
∴ The work done by Brandon in 1 day = 1/87 part
Now, the work done by Larry, Scott, and Brandon together in 1 day
= Larry's 1 day work + Scott's 1 day work + Brandon's 1 day work
= 1/77 + 1/82 + 1/87
= 7134 + 6699 + 6314/549318
= 20147/549318 part of work
This means in 1 day, 20147/549318 part of work is done by Larry, Scott and Brandon working together.
Now, the number of days required to finish 20147/549318 part of work by Larry, Scott, and Brandon working together = 1
∴ the number of days required to finish the whole work (1 work) by Larry + Scott + Brandon together
= 1/20147/549318
= 1 × 549318/20147 = 549318/20147 days
= 27 5349/20147 days = or 27.265 days
Thus, Larry, Scott, and Brandon working together will finish the total work (1 work) in 27 5349/20147 days = or 27.265 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 Larry = 77 days
And the number of days required to finish the same work by Scott = 82 days
And the number of days required to finish the work by Brandon = 87 days
Thus, the number of days required to finish the work by Larry, Scott, and Brandon together = ?
Here a = 77 days
And, b = 82 days
And, c = 87 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Larry, Scott, and Brandon working together
= 77 × 82 × 87/77 × 82 + 77 × 87 + 82 × 87 days
= 549318/6314 + 6699 + 7134 days
= 549318/20147 days
= 549318/20147 days
= 27 5349/20147 days or 27.265
Thus, Larry, Scott, and Brandon together will finish the work in 27 5349/20147 days or 27.265 days Answer
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