Question:
Brandon can finish a work in 83 days. Samuel can finish the same work in 88 days while Gregory can finish the work in 93 days. How long will it take to finish it if they work together?
Correct Answer
29 6269/23207 days or 29.27 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Brandon = 83 days
And, the number of days required to finish the same work by Samuel = 88 days
And, the number of days required to finish the same work by Gregory = 93 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 83 days the work is done by Brandon = 1
∴ The work done by Brandon in 1 day = 1/83
Similarly,
∵ In 88 days the work is done by Samuel = 1
∴ The work done by Samuel in 1 day = 1/88
Similarly,
∵ In 93 days the work is done by Gregory = 1
∴ The work done by Gregory in 1 day = 1/93 part
Now, the work done by Brandon, Samuel, and Gregory together in 1 day
= Brandon's 1 day work + Samuel's 1 day work + Gregory's 1 day work
= 1/83 + 1/88 + 1/93
= 8184 + 7719 + 7304/679272
= 23207/679272 part of work
This means in 1 day, 23207/679272 part of work is done by Brandon, Samuel and Gregory working together.
Now, the number of days required to finish 23207/679272 part of work by Brandon, Samuel, and Gregory working together = 1
∴ the number of days required to finish the whole work (1 work) by Brandon + Samuel + Gregory together
= 1/23207/679272
= 1 × 679272/23207 = 679272/23207 days
= 29 6269/23207 days = or 29.27 days
Thus, Brandon, Samuel, and Gregory working together will finish the total work (1 work) in 29 6269/23207 days = or 29.27 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 Brandon = 83 days
And the number of days required to finish the same work by Samuel = 88 days
And the number of days required to finish the work by Gregory = 93 days
Thus, the number of days required to finish the work by Brandon, Samuel, and Gregory together = ?
Here a = 83 days
And, b = 88 days
And, c = 93 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Brandon, Samuel, and Gregory working together
= 83 × 88 × 93/83 × 88 + 83 × 93 + 88 × 93 days
= 679272/7304 + 7719 + 8184 days
= 679272/23207 days
= 679272/23207 days
= 29 6269/23207 days or 29.27
Thus, Brandon, Samuel, and Gregory together will finish the work in 29 6269/23207 days or 29.27 days Answer
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