Question:
If Justin can finish the work in 79 days and Jesse can finish the same work in 84 days, then in how many days both can finish the work together?
Correct Answer
40 116/163 days or 40.712 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Justin = 79 days
And, the number of days to finish the same work by Jesse = 84 days
Thus, the number of days to finish the work by Justin and Jesse together = ?
Here,
∵ In 79 days the work done by Justin = 1
∴ In 1 day, the work done by Justin = 1/79 part
Similarly,
∵ In 84 days the work done by Jesse = 1
∴ In 1 day, the work done by Jesse = 1/84 part
Now, in 1 day, the work done by Justin and Jesse together
= In 1 day work done by Justin + In 1 day the work done by Jesse
= 1/79 + 1/84
= 84 + 79/6636
= 163/6636 part of work
This means in 1 day, 163/6636 part of work is done by Justin and Jesse working together.
Now, the number of days required to finish 163/6636 part of work by Justin + Jesse working together = 1
∴ the number of days required to finish 1 work by Justin + Jesse together
= 1/163/6636
= 1 × 6636/163 = 6636/163 days
= 40 116/163 days = or 40.712 days
Thus, Justin and Jesse working together will finish the work in 40 116/163 days = or 40.712 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, and B can finish the same work in b days,
then working together the number of days require to finish the work
= a × b/a + b 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 Jesse = 84 days
Thus, the number of days required to finish the work Justin and Jesse working together = ?
Here a = 79 days
And, b = 84 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Justin and Jesse working together
= 79 × 84/79 + 84 days
= 6636/163 days
= 40 116/163 days or 40.712
Thus, Justin and Jesse together will finish the work in 40 116/163 days or 40.712 days Answer
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