Question:
Justin can finish a work in 79 days. Brandon can finish the same work in 84 days while Benjamin can finish the work in 89 days. How long will it take to finish it if they work together?
Correct Answer
27 19743/21143 days or 27.934 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Justin = 79 days
And, the number of days required to finish the same work by Brandon = 84 days
And, the number of days required to finish the same work by Benjamin = 89 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 79 days the work is done by Justin = 1
∴ The work done by Justin in 1 day = 1/79
Similarly,
∵ In 84 days the work is done by Brandon = 1
∴ The work done by Brandon in 1 day = 1/84
Similarly,
∵ In 89 days the work is done by Benjamin = 1
∴ The work done by Benjamin in 1 day = 1/89 part
Now, the work done by Justin, Brandon, and Benjamin together in 1 day
= Justin's 1 day work + Brandon's 1 day work + Benjamin's 1 day work
= 1/79 + 1/84 + 1/89
= 7476 + 7031 + 6636/590604
= 21143/590604 part of work
This means in 1 day, 21143/590604 part of work is done by Justin, Brandon and Benjamin working together.
Now, the number of days required to finish 21143/590604 part of work by Justin, Brandon, and Benjamin working together = 1
∴ the number of days required to finish the whole work (1 work) by Justin + Brandon + Benjamin together
= 1/21143/590604
= 1 × 590604/21143 = 590604/21143 days
= 27 19743/21143 days = or 27.934 days
Thus, Justin, Brandon, and Benjamin working together will finish the total work (1 work) in 27 19743/21143 days = or 27.934 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 Justin = 79 days
And the number of days required to finish the same work by Brandon = 84 days
And the number of days required to finish the work by Benjamin = 89 days
Thus, the number of days required to finish the work by Justin, Brandon, and Benjamin together = ?
Here a = 79 days
And, b = 84 days
And, c = 89 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Justin, Brandon, and Benjamin working together
= 79 × 84 × 89/79 × 84 + 79 × 89 + 84 × 89 days
= 590604/6636 + 7031 + 7476 days
= 590604/21143 days
= 590604/21143 days
= 27 19743/21143 days or 27.934
Thus, Justin, Brandon, and Benjamin together will finish the work in 27 19743/21143 days or 27.934 days Answer
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