Question:
If Jennifer can finish the work in 7 days and Joseph can finish the same work in 11 days, then in how many days both can finish the work together?
Correct Answer
4 5/18 days or 4.278 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Jennifer = 7 days
And, the number of days to finish the same work by Joseph = 11 days
Thus, the number of days to finish the work by Jennifer and Joseph together = ?
Here,
∵ In 7 days the work done by Jennifer = 1
∴ In 1 day, the work done by Jennifer = 1/7 part
Similarly,
∵ In 11 days the work done by Joseph = 1
∴ In 1 day, the work done by Joseph = 1/11 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
= 1/7 + 1/11
= 11 + 7/77
= 18/77 part of work
This means in 1 day, 18/77 part of work is done by Jennifer and Joseph working together.
Now, the number of days required to finish 18/77 part of work by Jennifer + Joseph working together = 1
∴ the number of days required to finish 1 work by Jennifer + Joseph together
= 1/18/77
= 1 × 77/18 = 77/18 days
= 4 5/18 days = or 4.278 days
Thus, Jennifer and Joseph working together will finish the work in 4 5/18 days = or 4.278 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 = 7 days
And the number of days required to finish the same work by Joseph = 11 days
Thus, the number of days required to finish the work Jennifer and Joseph working together = ?
Here a = 7 days
And, b = 11 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Jennifer and Joseph working together
= 7 × 11/7 + 11 days
= 77/18 days
= 4 5/18 days or 4.278
Thus, Jennifer and Joseph together will finish the work in 4 5/18 days or 4.278 days Answer
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