Question:
If Elizabeth can finish the work in 11 days and Daniel can finish the same work in 15 days, then in how many days both can finish the work together?
Correct Answer
6 9/26 days or 6.346 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Elizabeth = 11 days
And, the number of days to finish the same work by Daniel = 15 days
Thus, the number of days to finish the work by Elizabeth and Daniel together = ?
Here,
∵ In 11 days the work done by Elizabeth = 1
∴ In 1 day, the work done by Elizabeth = 1/11 part
Similarly,
∵ In 15 days the work done by Daniel = 1
∴ In 1 day, the work done by Daniel = 1/15 part
Now, in 1 day, the work done by Elizabeth and Daniel together
= In 1 day work done by Elizabeth + In 1 day the work done by Daniel
= 1/11 + 1/15
= 15 + 11/165
= 26/165 part of work
This means in 1 day, 26/165 part of work is done by Elizabeth and Daniel working together.
Now, the number of days required to finish 26/165 part of work by Elizabeth + Daniel working together = 1
∴ the number of days required to finish 1 work by Elizabeth + Daniel together
= 1/26/165
= 1 × 165/26 = 165/26 days
= 6 9/26 days = or 6.346 days
Thus, Elizabeth and Daniel working together will finish the work in 6 9/26 days = or 6.346 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 Elizabeth = 11 days
And the number of days required to finish the same work by Daniel = 15 days
Thus, the number of days required to finish the work Elizabeth and Daniel working together = ?
Here a = 11 days
And, b = 15 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Elizabeth and Daniel working together
= 11 × 15/11 + 15 days
= 165/26 days
= 6 9/26 days or 6.346
Thus, Elizabeth and Daniel together will finish the work in 6 9/26 days or 6.346 days Answer
Similar Questions
(1) If Emily can finish the work in 37 days and Justin can finish the same work in 41 days, then in how many days both can finish the work together?
(2) Michael can finish a work in 11 days. William can finish the same work in 16 days while Richard can finish the work in 21 days. How long will it take to finish it if they work together?
(3) If Patricia can finish the work in 5 days and William can finish the same work in 9 days, then in how many days both can finish the work together?
(4) If Edward can finish the work in 57 days and Nathan can finish the same work in 62 days, then in how many days both can finish the work together?
(5) If Matthew can finish the work in 29 days and Edward can finish the same work in 34 days, then in how many days both can finish the work together?
(6) If Stephen can finish the work in 75 days and Carl can finish the same work in 80 days, then in how many days both can finish the work together?
(7) If Melissa can finish the work in 52 days and Jerry can finish the same work in 57 days, then in how many days both can finish the work together?
(8) 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?
(9) If Matthew can finish the work in 26 days and Edward can finish the same work in 30 days, then in how many days both can finish the work together?
(10) Dorothy can finish a work in 46 days. Melissa can finish the same work in 47 days while Deborah can finish the work in 48 days. How long will it take to finish it if they work together?