Question:
If Donna can finish the work in 39 days and Brandon can finish the same work in 43 days, then in how many days both can finish the work together?
Correct Answer
20 37/82 days or 20.451 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Donna = 39 days
And, the number of days to finish the same work by Brandon = 43 days
Thus, the number of days to finish the work by Donna and Brandon together = ?
Here,
∵ In 39 days the work done by Donna = 1
∴ In 1 day, the work done by Donna = 1/39 part
Similarly,
∵ In 43 days the work done by Brandon = 1
∴ In 1 day, the work done by Brandon = 1/43 part
Now, in 1 day, the work done by Donna and Brandon together
= In 1 day work done by Donna + In 1 day the work done by Brandon
= 1/39 + 1/43
= 43 + 39/1677
= 82/1677 part of work
This means in 1 day, 82/1677 part of work is done by Donna and Brandon working together.
Now, the number of days required to finish 82/1677 part of work by Donna + Brandon working together = 1
∴ the number of days required to finish 1 work by Donna + Brandon together
= 1/82/1677
= 1 × 1677/82 = 1677/82 days
= 20 37/82 days = or 20.451 days
Thus, Donna and Brandon working together will finish the work in 20 37/82 days = or 20.451 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 Donna = 39 days
And the number of days required to finish the same work by Brandon = 43 days
Thus, the number of days required to finish the work Donna and Brandon working together = ?
Here a = 39 days
And, b = 43 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Donna and Brandon working together
= 39 × 43/39 + 43 days
= 1677/82 days
= 20 37/82 days or 20.451
Thus, Donna and Brandon together will finish the work in 20 37/82 days or 20.451 days Answer
Similar Questions
(1) Elizabeth can finish a work in 10 days. Barbara can finish the same work in 11 days while Susan can finish the work in 12 days. How long will it take to finish it if they work together?
(2) If Robert can finish the work in 7 days and David can finish the same work in 12 days, then in how many days both can finish the work together?
(3) If Donna can finish the work in 39 days and Brandon can finish the same work in 43 days, then in how many days both can finish the work together?
(4) If Donald can finish the work in 32 days and Nicholas can finish the same work in 36 days, then in how many days both can finish the work together?
(5) If Kenneth can finish the work in 42 days and Gregory can finish the same work in 46 days, then in how many days both can finish the work together?
(6) If Daniel can finish the work in 27 days and Timothy can finish the same work in 32 days, then in how many days both can finish the work together?
(7) If Patricia can finish the work in 5 days and William can finish the same work in 9 days, then in how many days both can finish the work together?
(8) Barbara can finish a work in 16 days. Jessica can finish the same work in 21 days while Sarah can finish the work in 26 days. How long will it take to finish it if they work together?
(9) Elizabeth can finish a work in 14 days. Susan can finish the same work in 19 days while Jessica can finish the work in 24 days. How long will it take to finish it if they work together?
(10) If Linda can finish the work in 31 days and Charles can finish the same work in 47 days, then in how many days both can finish the work together?