Question:
If Patricia can finish the work in 5 days and William can finish the same work in 8 days, then in how many days both can finish the work together?
Correct Answer
3 1/13 days or 3.077 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Patricia = 5 days
And, the number of days to finish the same work by William = 8 days
Thus, the number of days to finish the work by Patricia and William together = ?
Here,
∵ In 5 days the work done by Patricia = 1
∴ In 1 day, the work done by Patricia = 1/5 part
Similarly,
∵ In 8 days the work done by William = 1
∴ In 1 day, the work done by William = 1/8 part
Now, in 1 day, the work done by Patricia and William together
= In 1 day work done by Patricia + In 1 day the work done by William
= 1/5 + 1/8
= 8 + 5/40
= 13/40 part of work
This means in 1 day, 13/40 part of work is done by Patricia and William working together.
Now, the number of days required to finish 13/40 part of work by Patricia + William working together = 1
∴ the number of days required to finish 1 work by Patricia + William together
= 1/13/40
= 1 × 40/13 = 40/13 days
= 3 1/13 days = or 3.077 days
Thus, Patricia and William working together will finish the work in 3 1/13 days = or 3.077 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 Patricia = 5 days
And the number of days required to finish the same work by William = 8 days
Thus, the number of days required to finish the work Patricia and William working together = ?
Here a = 5 days
And, b = 8 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Patricia and William working together
= 5 × 8/5 + 8 days
= 40/13 days
= 3 1/13 days or 3.077
Thus, Patricia and William together will finish the work in 3 1/13 days or 3.077 days Answer
Similar Questions
(1) If Amanda can finish the work in 48 days and Patrick can finish the same work in 53 days, then in how many days both can finish the work together?
(2) If William can finish the work in 34 days and Matthew can finish the same work in 50 days, then in how many days both can finish the work together?
(3) Janet can finish a work in 98 days. Maria can finish the same work in 103 days while Heather can finish the work in 108 days. How long will it take to finish it if they work together?
(4) If Betty can finish the work in 27 days and Jason can finish the same work in 31 days, then in how many days both can finish the work together?
(5) 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?
(6) John can finish a work in 5 days. Michael can finish the same work in 6 days while David can finish the work in 7 days. How long will it take to finish it if they work together?
(7) If Anthony can finish the work in 28 days and Jeffrey can finish the same work in 32 days, then in how many days both can finish the work together?
(8) If Ronald can finish the work in 55 days and Jose can finish the same work in 60 days, then in how many days both can finish the work together?
(9) 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?
(10) If A can do a piece of work in 2 days, B can do the same piece of work in 3 days, while C alone can do the same work in 4 days. Find the number of days to finish the work when they all will work together.