Question:
If Ryan can finish the work in 63 days and Ethan can finish the same work in 68 days, then in how many days both can finish the work together?
Correct Answer
32 92/131 days or 32.702 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Ryan = 63 days
And, the number of days to finish the same work by Ethan = 68 days
Thus, the number of days to finish the work by Ryan and Ethan together = ?
Here,
∵ In 63 days the work done by Ryan = 1
∴ In 1 day, the work done by Ryan = 1/63 part
Similarly,
∵ In 68 days the work done by Ethan = 1
∴ In 1 day, the work done by Ethan = 1/68 part
Now, in 1 day, the work done by Ryan and Ethan together
= In 1 day work done by Ryan + In 1 day the work done by Ethan
= 1/63 + 1/68
= 68 + 63/4284
= 131/4284 part of work
This means in 1 day, 131/4284 part of work is done by Ryan and Ethan working together.
Now, the number of days required to finish 131/4284 part of work by Ryan + Ethan working together = 1
∴ the number of days required to finish 1 work by Ryan + Ethan together
= 1/131/4284
= 1 × 4284/131 = 4284/131 days
= 32 92/131 days = or 32.702 days
Thus, Ryan and Ethan working together will finish the work in 32 92/131 days = or 32.702 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 Ryan = 63 days
And the number of days required to finish the same work by Ethan = 68 days
Thus, the number of days required to finish the work Ryan and Ethan working together = ?
Here a = 63 days
And, b = 68 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Ryan and Ethan working together
= 63 × 68/63 + 68 days
= 4284/131 days
= 32 92/131 days or 32.702
Thus, Ryan and Ethan together will finish the work in 32 92/131 days or 32.702 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 Pamela can finish the work in 78 days and Dylan can finish the same work in 83 days, then in how many days both can finish the work together?
(3) If Kevin can finish the work in 47 days and Frank can finish the same work in 52 days, then in how many days both can finish the work together?
(4) 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?
(5) If Charles can finish the work in 20 days and Kenneth can finish the same work in 24 days, then in how many days both can finish the work together?
(6) If Timothy can finish the work in 53 days and Tyler can finish the same work in 58 days, then in how many days both can finish the work together?
(7) Margaret can finish a work in 32 days. Ashley can finish the same work in 37 days while Kimberly can finish the work in 42 days. How long will it take to finish it if they work together?
(8) 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?
(9) If Betty can finish the work in 30 days and Jason can finish the same work in 35 days, then in how many days both can finish the work together?
(10) Michelle can finish a work in 40 days. Carol can finish the same work in 41 days while Amanda can finish the work in 42 days. How long will it take to finish it if they work together?