Question:
If Jessica can finish the work in 17 days and Paul can finish the same work in 21 days, then in how many days both can finish the work together?
Correct Answer
9 15/38 days or 9.395 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Jessica = 17 days
And, the number of days to finish the same work by Paul = 21 days
Thus, the number of days to finish the work by Jessica and Paul together = ?
Here,
∵ In 17 days the work done by Jessica = 1
∴ In 1 day, the work done by Jessica = 1/17 part
Similarly,
∵ In 21 days the work done by Paul = 1
∴ In 1 day, the work done by Paul = 1/21 part
Now, in 1 day, the work done by Jessica and Paul together
= In 1 day work done by Jessica + In 1 day the work done by Paul
= 1/17 + 1/21
= 21 + 17/357
= 38/357 part of work
This means in 1 day, 38/357 part of work is done by Jessica and Paul working together.
Now, the number of days required to finish 38/357 part of work by Jessica + Paul working together = 1
∴ the number of days required to finish 1 work by Jessica + Paul together
= 1/38/357
= 1 × 357/38 = 357/38 days
= 9 15/38 days = or 9.395 days
Thus, Jessica and Paul working together will finish the work in 9 15/38 days = or 9.395 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 Jessica = 17 days
And the number of days required to finish the same work by Paul = 21 days
Thus, the number of days required to finish the work Jessica and Paul working together = ?
Here a = 17 days
And, b = 21 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Jessica and Paul working together
= 17 × 21/17 + 21 days
= 357/38 days
= 9 15/38 days or 9.395
Thus, Jessica and Paul together will finish the work in 9 15/38 days or 9.395 days Answer
Similar Questions
(1) If A can finish a work in 10 days and B can finish the same work in 15 days, then in how many days they both can finish the work working together?
(2) 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?
(3) If Robert can finish the work in 7 days and David can finish the same work in 12 days, then in how many days both can finish the work together?
(4) Kevin can finish a work in 43 days. Brian can finish the same work in 44 days while George can finish the work in 45 days. How long will it take to finish it if they work together?
(5) 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?
(6) If Richard can finish the work in 36 days and Mark can finish the same work in 52 days, then in how many days both can finish the work together?
(7) Samuel can finish a work in 87 days. Alexander can finish the same work in 92 days while Frank can finish the work in 97 days. How long will it take to finish it if they work together?
(8) If Cynthia can finish the work in 64 days and Walter can finish the same work in 69 days, then in how many days both can finish the work together?
(9) If Paul can finish the work in 36 days and Larry can finish the same work in 40 days, then in how many days both can finish the work together?
(10) If Amanda can finish the work in 45 days and Patrick can finish the same work in 48 days, then in how many days both can finish the work together?