Question:
If Sandra can finish the work in 34 days and Gary can finish the same work in 39 days, then in how many days both can finish the work together?
Correct Answer
18 12/73 days or 18.164 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Sandra = 34 days
And, the number of days to finish the same work by Gary = 39 days
Thus, the number of days to finish the work by Sandra and Gary together = ?
Here,
∵ In 34 days the work done by Sandra = 1
∴ In 1 day, the work done by Sandra = 1/34 part
Similarly,
∵ In 39 days the work done by Gary = 1
∴ In 1 day, the work done by Gary = 1/39 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
= 1/34 + 1/39
= 39 + 34/1326
= 73/1326 part of work
This means in 1 day, 73/1326 part of work is done by Sandra and Gary working together.
Now, the number of days required to finish 73/1326 part of work by Sandra + Gary working together = 1
∴ the number of days required to finish 1 work by Sandra + Gary together
= 1/73/1326
= 1 × 1326/73 = 1326/73 days
= 18 12/73 days = or 18.164 days
Thus, Sandra and Gary working together will finish the work in 18 12/73 days = or 18.164 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 = 34 days
And the number of days required to finish the same work by Gary = 39 days
Thus, the number of days required to finish the work Sandra and Gary working together = ?
Here a = 34 days
And, b = 39 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Sandra and Gary working together
= 34 × 39/34 + 39 days
= 1326/73 days
= 18 12/73 days or 18.164
Thus, Sandra and Gary together will finish the work in 18 12/73 days or 18.164 days Answer
Similar Questions
(1) Ashley can finish a work in 36 days. Emily can finish the same work in 41 days while Donna can finish the work in 46 days. How long will it take to finish it if they work together?
(2) Debra can finish a work in 92 days. Carolyn can finish the same work in 97 days while Janet can finish the work in 102 days. How long will it take to finish it if they work together?
(3) If Emily can finish the work in 40 days and Justin can finish the same work in 45 days, then in how many days both can finish the work together?
(4) If Katherine can finish the work in 88 days and Willie can finish the same work in 93 days, then in how many days both can finish the work together?
(5) William can finish a work in 11 days. Richard can finish the same work in 12 days while Joseph can finish the work in 13 days. How long will it take to finish it if they work together?
(6) Christine can finish a work in 90 days. Rachel can finish the same work in 95 days while Carolyn can finish the work in 100 days. How long will it take to finish it if they work together?
(7) Donald can finish a work in 35 days. Paul can finish the same work in 40 days while Andrew can finish the work in 45 days. How long will it take to finish it if they work together?
(8) If Matthew can finish the work in 26 days and Edward can finish the same work in 29 days, then in how many days both can finish the work together?
(9) If Sarah can finish the work in 19 days and Joshua can finish the same work in 23 days, then in how many days both can finish the work together?
(10) Jennifer can finish a work in 10 days. Elizabeth can finish the same work in 15 days while Barbara can finish the work in 20 days. How long will it take to finish it if they work together?