Question:
If Sandra can finish the work in 31 days and Gary can finish the same work in 35 days, then in how many days both can finish the work together?
Correct Answer
16 29/66 days or 16.439 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Sandra = 31 days
And, the number of days to finish the same work by Gary = 35 days
Thus, the number of days to finish the work by Sandra and Gary together = ?
Here,
∵ In 31 days the work done by Sandra = 1
∴ In 1 day, the work done by Sandra = 1/31 part
Similarly,
∵ In 35 days the work done by Gary = 1
∴ In 1 day, the work done by Gary = 1/35 part
Now, in 1 day, the work done by Sandra and Gary together
= In 1 day work done by Sandra + In 1 day the work done by Gary
= 1/31 + 1/35
= 35 + 31/1085
= 66/1085 part of work
This means in 1 day, 66/1085 part of work is done by Sandra and Gary working together.
Now, the number of days required to finish 66/1085 part of work by Sandra + Gary working together = 1
∴ the number of days required to finish 1 work by Sandra + Gary together
= 1/66/1085
= 1 × 1085/66 = 1085/66 days
= 16 29/66 days = or 16.439 days
Thus, Sandra and Gary working together will finish the work in 16 29/66 days = or 16.439 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 Sandra = 31 days
And the number of days required to finish the same work by Gary = 35 days
Thus, the number of days required to finish the work Sandra and Gary working together = ?
Here a = 31 days
And, b = 35 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Sandra and Gary working together
= 31 × 35/31 + 35 days
= 1085/66 days
= 16 29/66 days or 16.439
Thus, Sandra and Gary together will finish the work in 16 29/66 days or 16.439 days Answer
Similar Questions
(1) 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?
(2) If Elizabeth can finish the work in 33 days and Daniel can finish the same work in 49 days, then in how many days both can finish the work together?
(3) If Linda can finish the work in 9 days and Charles can finish the same work in 12 days, then in how many days both can finish the work together?
(4) If Thomas can finish the work in 21 days and Andrew can finish the same work in 26 days, then in how many days both can finish the work together?
(5) 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.
(6) Paul can finish a work in 35 days. Andrew can finish the same work in 36 days while Joshua can finish the work in 37 days. How long will it take to finish it if they work together?
(7) Gregory can finish a work in 89 days. Frank can finish the same work in 94 days while Patrick can finish the work in 99 days. How long will it take to finish it if they work together?
(8) Mark can finish a work in 33 days. Steven can finish the same work in 38 days while Paul can finish the work in 43 days. How long will it take to finish it if they work together?
(9) Sandra can finish a work in 34 days. Kimberly can finish the same work in 39 days while Emily can finish the work in 44 days. How long will it take to finish it if they work together?
(10) Stephanie can finish a work in 56 days. Sharon can finish the same work in 61 days while Laura can finish the work in 66 days. How long will it take to finish it if they work together?