Question:
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?
Correct Answer
29 83/119 days or 29.697 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Edward = 57 days
And, the number of days to finish the same work by Nathan = 62 days
Thus, the number of days to finish the work by Edward and Nathan together = ?
Here,
∵ In 57 days the work done by Edward = 1
∴ In 1 day, the work done by Edward = 1/57 part
Similarly,
∵ In 62 days the work done by Nathan = 1
∴ In 1 day, the work done by Nathan = 1/62 part
Now, in 1 day, the work done by Edward and Nathan together
= In 1 day work done by Edward + In 1 day the work done by Nathan
= 1/57 + 1/62
= 62 + 57/3534
= 119/3534 part of work
This means in 1 day, 119/3534 part of work is done by Edward and Nathan working together.
Now, the number of days required to finish 119/3534 part of work by Edward + Nathan working together = 1
∴ the number of days required to finish 1 work by Edward + Nathan together
= 1/119/3534
= 1 × 3534/119 = 3534/119 days
= 29 83/119 days = or 29.697 days
Thus, Edward and Nathan working together will finish the work in 29 83/119 days = or 29.697 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 Edward = 57 days
And the number of days required to finish the same work by Nathan = 62 days
Thus, the number of days required to finish the work Edward and Nathan working together = ?
Here a = 57 days
And, b = 62 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Edward and Nathan working together
= 57 × 62/57 + 62 days
= 3534/119 days
= 29 83/119 days or 29.697
Thus, Edward and Nathan together will finish the work in 29 83/119 days or 29.697 days Answer
Similar Questions
(1) If Gregory can finish the work in 89 days and Alan can finish the same work in 94 days, then in how many days both can finish the work together?
(2) If David can finish the work in 13 days and Christopher can finish the same work in 18 days, then in how many days both can finish the work together?
(3) Janet can finish a work in 98 days. Maria can finish the same work in 103 days while Heather can finish the work in 108 days. How long will it take to finish it if they 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) If Anthony can finish the work in 28 days and Jeffrey can finish the same work in 31 days, then in how many days both can finish the work together?
(6) 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?
(7) If Mary can finish the work in 6 days and Michael can finish the same work in 11 days, then in how many days both can finish the work together?
(8) Kevin can finish a work in 47 days. George can finish the same work in 52 days while Timothy can finish the work in 57 days. How long will it take to finish it if they work together?
(9) If Stephanie can finish the work in 56 days and Adam can finish the same work in 61 days, then in how many days both can finish the work together?
(10) If Samuel can finish the work in 87 days and Albert can finish the same work in 92 days, then in how many days both can finish the work together?