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
Similar Questions
(1) Sandra can finish a work in 30 days. Ashley can finish the same work in 31 days while Kimberly can finish the work in 32 days. How long will it take to finish it if they work together?
(2) If Christine can finish the work in 90 days and Juan can finish the same work in 95 days, then in how many days both can finish the work together?
(3) If Ashley can finish the work in 33 days and Eric can finish the same work in 37 days, then in how many days both can finish the work together?
(4) If Jack can finish the work in 20 days and Bill can finish the same work in 30 days, then in how many days they both can finish the work working together?
(5) If Brian can finish the work in 46 days and Raymond can finish the same work in 50 days, then in how many days both can finish the work together?
(6) If Patricia can finish the work in 27 days and William can finish the same work in 43 days, then in how many days both can finish the work together?
(7) Jessica can finish a work in 16 days. Sarah can finish the same work in 17 days while Karen can finish the work in 18 days. How long will it take to finish it if they work together?
(8) Timothy can finish a work in 53 days. Edward can finish the same work in 58 days while Jason can finish the work in 63 days. How long will it take to finish it if they work together?
(9) If Richard can finish the work in 14 days and Mark can finish the same work in 18 days, then in how many days both can finish the work together?
(10) If Robert can finish the work in 4 days and David can finish the same work in 7 days, then in how many days both can finish the work together?