Question:
If Jennifer can finish the work in 7 days and Joseph can finish the same work in 10 days, then in how many days both can finish the work together?
Correct Answer
4 2/17 days or 4.118 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 = 10 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 10 days the work done by Joseph = 1
∴ In 1 day, the work done by Joseph = 1/10 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 + 1/10
= 10 + 7/70
= 17/70 part of work
This means in 1 day, 17/70 part of work is done by Jennifer and Joseph working together.
Now, the number of days required to finish 17/70 part of work by Jennifer + Joseph working together = 1
∴ the number of days required to finish 1 work by Jennifer + Joseph together
= 1/17/70
= 1 × 70/17 = 70/17 days
= 4 2/17 days = or 4.118 days
Thus, Jennifer and Joseph working together will finish the work in 4 2/17 days = or 4.118 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 = 10 days
Thus, the number of days required to finish the work Jennifer and Joseph working together = ?
Here a = 7 days
And, b = 10 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 × 10/7 + 10 days
= 70/17 days
= 4 2/17 days or 4.118
Thus, Jennifer and Joseph together will finish the work in 4 2/17 days or 4.118 days Answer
Similar Questions
(1) If Michael can finish the work in 11 days and Thomas can finish the same work in 16 days, then in how many days both can finish the work together?
(2) If Joseph can finish the work in 16 days and Steven can finish the same work in 19 days, then in how many days both can finish the work together?
(3) If Lisa can finish the work in 26 days and George can finish the same work in 31 days, then in how many days both can finish the work together?
(4) Nancy can finish a work in 24 days. Betty can finish the same work in 25 days while Margaret can finish the work in 26 days. How long will it take to finish it if they work together?
(5) 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?
(6) If Anthony can finish the work in 31 days and Jeffrey can finish the same work in 36 days, then in how many days both can finish the work together?
(7) Edward can finish a work in 57 days. Jeffrey can finish the same work in 62 days while Ryan can finish the work in 67 days. How long will it take to finish it if they work together?
(8) If Steven can finish the work in 37 days and Jonathan can finish the same work in 42 days, then in how many days both can finish the work together?
(9) Carolyn can finish a work in 96 days. Catherine can finish the same work in 101 days while Maria can finish the work in 106 days. How long will it take to finish it if they work together?
(10) Nicholas can finish a work in 69 days. Jonathan can finish the same work in 74 days while Stephen can finish the work in 79 days. How long will it take to finish it if they work together?