Question:
If Patricia can finish the work in 8 days and William can finish the same work in 13 days, then in how many days both can finish the work together?
Correct Answer
4 20/21 days or 4.952 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Patricia = 8 days
And, the number of days to finish the same work by William = 13 days
Thus, the number of days to finish the work by Patricia and William together = ?
Here,
∵ In 8 days the work done by Patricia = 1
∴ In 1 day, the work done by Patricia = 1/8 part
Similarly,
∵ In 13 days the work done by William = 1
∴ In 1 day, the work done by William = 1/13 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
= 1/8 + 1/13
= 13 + 8/104
= 21/104 part of work
This means in 1 day, 21/104 part of work is done by Patricia and William working together.
Now, the number of days required to finish 21/104 part of work by Patricia + William working together = 1
∴ the number of days required to finish 1 work by Patricia + William together
= 1/21/104
= 1 × 104/21 = 104/21 days
= 4 20/21 days = or 4.952 days
Thus, Patricia and William working together will finish the work in 4 20/21 days = or 4.952 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 = 8 days
And the number of days required to finish the same work by William = 13 days
Thus, the number of days required to finish the work Patricia and William working together = ?
Here a = 8 days
And, b = 13 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Patricia and William working together
= 8 × 13/8 + 13 days
= 104/21 days
= 4 20/21 days or 4.952
Thus, Patricia and William together will finish the work in 4 20/21 days or 4.952 days Answer
Similar Questions
(1) If Annie can finish a work in 3 days and Bobby can finish the same work in 6 days, then in how many days they both can finish the work working together?
(2) Linda can finish a work in 8 days. Elizabeth can finish the same work in 9 days while Barbara can finish the work in 10 days. How long will it take to finish it if they work together?
(3) Emily can finish a work in 40 days. Michelle can finish the same work in 45 days while Carol can finish the work in 50 days. How long will it take to finish it if they work together?
(4) Daniel can finish a work in 23 days. Matthew can finish the same work in 24 days while Anthony can finish the work in 25 days. How long will it take to finish it if they work together?
(5) Emily can finish a work in 36 days. Donna can finish the same work in 37 days while Michelle can finish the work in 38 days. How long will it take to finish it if they work together?
(6) If Michelle can finish the work in 44 days and Samuel can finish the same work in 49 days, then in how many days both can finish the work together?
(7) Pamela can finish a work in 78 days. Nicole can finish the same work in 83 days while Helen can finish the work in 88 days. How long will it take to finish it if they work together?
(8) If Andrew can finish the work in 38 days and Scott can finish the same work in 41 days, then in how many days both can finish the work together?
(9) If Kevin can finish the work in 44 days and Frank can finish the same work in 48 days, then in how many days both can finish the work together?
(10) Robert can finish a work in 3 days. John can finish the same work in 4 days while Michael can finish the work in 5 days. How long will it take to finish it if they work together?