Question:
If Jennifer can finish the work in 29 days and Joseph can finish the same work in 45 days, then in how many days both can finish the work together?
Correct Answer
17 47/74 days or 17.635 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Jennifer = 29 days
And, the number of days to finish the same work by Joseph = 45 days
Thus, the number of days to finish the work by Jennifer and Joseph together = ?
Here,
∵ In 29 days the work done by Jennifer = 1
∴ In 1 day, the work done by Jennifer = 1/29 part
Similarly,
∵ In 45 days the work done by Joseph = 1
∴ In 1 day, the work done by Joseph = 1/45 part
Now, in 1 day, the work done by Jennifer and Joseph together
= In 1 day work done by Jennifer + In 1 day the work done by Joseph
= 1/29 + 1/45
= 45 + 29/1305
= 74/1305 part of work
This means in 1 day, 74/1305 part of work is done by Jennifer and Joseph working together.
Now, the number of days required to finish 74/1305 part of work by Jennifer + Joseph working together = 1
∴ the number of days required to finish 1 work by Jennifer + Joseph together
= 1/74/1305
= 1 × 1305/74 = 1305/74 days
= 17 47/74 days = or 17.635 days
Thus, Jennifer and Joseph working together will finish the work in 17 47/74 days = or 17.635 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 Jennifer = 29 days
And the number of days required to finish the same work by Joseph = 45 days
Thus, the number of days required to finish the work Jennifer and Joseph working together = ?
Here a = 29 days
And, b = 45 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Jennifer and Joseph working together
= 29 × 45/29 + 45 days
= 1305/74 days
= 17 47/74 days or 17.635
Thus, Jennifer and Joseph together will finish the work in 17 47/74 days or 17.635 days Answer
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