Question:
If Kevin can finish the work in 44 days and Frank can finish the same work in 48 days, then in how many days both can finish the work together?
Correct Answer
22 22/23 days or 22.957 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Kevin = 44 days
And, the number of days to finish the same work by Frank = 48 days
Thus, the number of days to finish the work by Kevin and Frank together = ?
Here,
∵ In 44 days the work done by Kevin = 1
∴ In 1 day, the work done by Kevin = 1/44 part
Similarly,
∵ In 48 days the work done by Frank = 1
∴ In 1 day, the work done by Frank = 1/48 part
Now, in 1 day, the work done by Kevin and Frank together
= In 1 day work done by Kevin + In 1 day the work done by Frank
= 1/44 + 1/48
= 12 + 11/528
= 23/528 part of work
This means in 1 day, 23/528 part of work is done by Kevin and Frank working together.
Now, the number of days required to finish 23/528 part of work by Kevin + Frank working together = 1
∴ the number of days required to finish 1 work by Kevin + Frank together
= 1/23/528
= 1 × 528/23 = 528/23 days
= 22 22/23 days = or 22.957 days
Thus, Kevin and Frank working together will finish the work in 22 22/23 days = or 22.957 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 Kevin = 44 days
And the number of days required to finish the same work by Frank = 48 days
Thus, the number of days required to finish the work Kevin and Frank working together = ?
Here a = 44 days
And, b = 48 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Kevin and Frank working together
= 44 × 48/44 + 48 days
= 2112/92 days
= 2112 ÷ 4/92 ÷ 4 = 528/23 days
= 22 22/23 days or 22.957
Thus, Kevin and Frank together will finish the work in 22 22/23 days or 22.957 days Answer
Similar Questions
(1) If Donna can finish the work in 39 days and Brandon can finish the same work in 42 days, then in how many days both can finish the work together?
(2) Donna can finish a work in 42 days. Carol can finish the same work in 47 days while Amanda can finish the work in 52 days. How long will it take to finish it if they work together?
(3) Barbara can finish a work in 12 days. Susan can finish the same work in 13 days while Jessica can finish the work in 14 days. How long will it take to finish it if they work together?
(4) If Anna can finish the work in 74 days and Austin can finish the same work in 79 days, then in how many days both can finish the work together?
(5) If Margaret can finish the work in 29 days and Ryan can finish the same work in 32 days, then in how many days both can finish the work together?
(6) 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?
(7) If Jason can finish the work in 59 days and Douglas can finish the same work in 64 days, then in how many days both can finish the work together?
(8) George can finish a work in 47 days. Timothy can finish the same work in 48 days while Ronald can finish the work in 49 days. How long will it take to finish it if they work together?
(9) 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?
(10) Jessica can finish a work in 20 days. Karen can finish the same work in 25 days while Lisa can finish the work in 30 days. How long will it take to finish it if they work together?