Question:
If Barbara can finish the work in 13 days and Anthony can finish the same work in 16 days, then in how many days both can finish the work together?
Correct Answer
7 5/29 days or 7.172 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Barbara = 13 days
And, the number of days to finish the same work by Anthony = 16 days
Thus, the number of days to finish the work by Barbara and Anthony together = ?
Here,
∵ In 13 days the work done by Barbara = 1
∴ In 1 day, the work done by Barbara = 1/13 part
Similarly,
∵ In 16 days the work done by Anthony = 1
∴ In 1 day, the work done by Anthony = 1/16 part
Now, in 1 day, the work done by Barbara and Anthony together
= In 1 day work done by Barbara + In 1 day the work done by Anthony
= 1/13 + 1/16
= 16 + 13/208
= 29/208 part of work
This means in 1 day, 29/208 part of work is done by Barbara and Anthony working together.
Now, the number of days required to finish 29/208 part of work by Barbara + Anthony working together = 1
∴ the number of days required to finish 1 work by Barbara + Anthony together
= 1/29/208
= 1 × 208/29 = 208/29 days
= 7 5/29 days = or 7.172 days
Thus, Barbara and Anthony working together will finish the work in 7 5/29 days = or 7.172 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 Barbara = 13 days
And the number of days required to finish the same work by Anthony = 16 days
Thus, the number of days required to finish the work Barbara and Anthony working together = ?
Here a = 13 days
And, b = 16 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Barbara and Anthony working together
= 13 × 16/13 + 16 days
= 208/29 days
= 7 5/29 days or 7.172
Thus, Barbara and Anthony together will finish the work in 7 5/29 days or 7.172 days Answer
Similar Questions
(1) Kevin can finish a work in 43 days. Brian can finish the same work in 44 days while George can finish the work in 45 days. How long will it take to finish it if they work together?
(2) If Jessica can finish the work in 20 days and Paul can finish the same work in 25 days, then in how many days both can finish the work together?
(3) If Annie can finish a work in 5 days and Bobby can finish the same work in 10 days, then in how many days they both can finish the work working together?
(4) If Elizabeth can finish the work in 14 days and Daniel can finish the same work in 19 days, then in how many days both can finish the work together?
(5) If Kimberly can finish the work in 35 days and Stephen can finish the same work in 39 days, then in how many days both can finish the work together?
(6) If Nancy can finish the work in 25 days and Ronald can finish the same work in 28 days, then in how many days both can finish the work together?
(7) If Eric can finish the work in 71 days and Gerald can finish the same work in 76 days, then in how many days both can finish the work together?
(8) If Karen can finish the work in 24 days and Kevin can finish the same work in 29 days, then in how many days both can finish the work together?
(9) If Sarah can finish the work in 19 days and Joshua can finish the same work in 23 days, then in how many days both can finish the work together?
(10) Melissa can finish a work in 52 days. Stephanie can finish the same work in 57 days while Rebecca can finish the work in 62 days. How long will it take to finish it if they work together?