Question:
If Cynthia can finish the work in 64 days and Walter can finish the same work in 69 days, then in how many days both can finish the work together?
Correct Answer
33 27/133 days or 33.203 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Cynthia = 64 days
And, the number of days to finish the same work by Walter = 69 days
Thus, the number of days to finish the work by Cynthia and Walter together = ?
Here,
∵ In 64 days the work done by Cynthia = 1
∴ In 1 day, the work done by Cynthia = 1/64 part
Similarly,
∵ In 69 days the work done by Walter = 1
∴ In 1 day, the work done by Walter = 1/69 part
Now, in 1 day, the work done by Cynthia and Walter together
= In 1 day work done by Cynthia + In 1 day the work done by Walter
= 1/64 + 1/69
= 69 + 64/4416
= 133/4416 part of work
This means in 1 day, 133/4416 part of work is done by Cynthia and Walter working together.
Now, the number of days required to finish 133/4416 part of work by Cynthia + Walter working together = 1
∴ the number of days required to finish 1 work by Cynthia + Walter together
= 1/133/4416
= 1 × 4416/133 = 4416/133 days
= 33 27/133 days = or 33.203 days
Thus, Cynthia and Walter working together will finish the work in 33 27/133 days = or 33.203 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 Cynthia = 64 days
And the number of days required to finish the same work by Walter = 69 days
Thus, the number of days required to finish the work Cynthia and Walter working together = ?
Here a = 64 days
And, b = 69 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Cynthia and Walter working together
= 64 × 69/64 + 69 days
= 4416/133 days
= 33 27/133 days or 33.203
Thus, Cynthia and Walter together will finish the work in 33 27/133 days or 33.203 days Answer
Similar Questions
(1) Nancy can finish a work in 28 days. Margaret can finish the same work in 33 days while Sandra can finish the work in 38 days. How long will it take to finish it if they work together?
(2) If Charles can finish the work in 23 days and Kenneth can finish the same work in 28 days, then in how many days both can finish the work together?
(3) If Brandon can finish the work in 83 days and Joe can finish the same work in 88 days, then in how many days both can finish the work together?
(4) If William can finish the work in 12 days and Matthew can finish the same work in 15 days, then in how many days both can finish the work together?
(5) If Mark can finish the work in 30 days and Jacob can finish the same work in 34 days, then in how many days both can finish the work together?
(6) If Patricia can finish the work in 27 days and William can finish the same work in 43 days, then in how many days both can finish the work together?
(7) 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?
(8) 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?
(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) If George can finish the work in 51 days and Dennis can finish the same work in 56 days, then in how many days both can finish the work together?