Question:
If Amanda can finish the work in 45 days and Patrick can finish the same work in 48 days, then in how many days both can finish the work together?
Correct Answer
23 7/31 days or 23.226 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Amanda = 45 days
And, the number of days to finish the same work by Patrick = 48 days
Thus, the number of days to finish the work by Amanda and Patrick together = ?
Here,
∵ In 45 days the work done by Amanda = 1
∴ In 1 day, the work done by Amanda = 1/45 part
Similarly,
∵ In 48 days the work done by Patrick = 1
∴ In 1 day, the work done by Patrick = 1/48 part
Now, in 1 day, the work done by Amanda and Patrick together
= In 1 day work done by Amanda + In 1 day the work done by Patrick
= 1/45 + 1/48
= 16 + 15/720
= 31/720 part of work
This means in 1 day, 31/720 part of work is done by Amanda and Patrick working together.
Now, the number of days required to finish 31/720 part of work by Amanda + Patrick working together = 1
∴ the number of days required to finish 1 work by Amanda + Patrick together
= 1/31/720
= 1 × 720/31 = 720/31 days
= 23 7/31 days = or 23.226 days
Thus, Amanda and Patrick working together will finish the work in 23 7/31 days = or 23.226 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 Amanda = 45 days
And the number of days required to finish the same work by Patrick = 48 days
Thus, the number of days required to finish the work Amanda and Patrick working together = ?
Here a = 45 days
And, b = 48 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Amanda and Patrick working together
= 45 × 48/45 + 48 days
= 2160/93 days
= 2160 ÷ 3/93 ÷ 3 = 720/31 days
= 23 7/31 days or 23.226
Thus, Amanda and Patrick together will finish the work in 23 7/31 days or 23.226 days Answer
Similar Questions
(1) If Annie can finish a work in 2 days and Bobby can finish the same work in 3 days, then in how many days they both can finish the work working together?
(2) If Mary can finish the work in 6 days and Michael can finish the same work in 11 days, then in how many days both can finish the work together?
(3) Sarah can finish a work in 18 days. Karen can finish the same work in 19 days while Lisa can finish the work in 20 days. How long will it take to finish it if they work together?
(4) If Catherine can finish the work in 100 days and Mason can finish the same work in 105 days, then in how many days both can finish the work together?
(5) If Donald can finish the work in 32 days and Nicholas can finish the same work in 35 days, then in how many days both can finish the work together?
(6) If Nicole can finish the work in 82 days and Billy can finish the same work in 87 days, then in how many days both can finish the work together?
(7) If Susan can finish the work in 15 days and Donald can finish the same work in 19 days, then in how many days both can finish the work together?
(8) If Steven can finish the work in 34 days and Jonathan can finish the same work in 37 days, then in how many days both can finish the work together?
(9) If Ashley can finish the work in 36 days and Eric can finish the same work in 41 days, then in how many days both can finish the work together?
(10) Matthew can finish a work in 25 days. Anthony can finish the same work in 26 days while Mark can finish the work in 27 days. How long will it take to finish it if they work together?