Question:
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?
Correct Answer
8 4/37 days or 8.108 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Jessica = 20 days
And, the number of days required to finish the same work by Karen = 25 days
And, the number of days required to finish the same work by Lisa = 30 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 20 days the work is done by Jessica = 1
∴ The work done by Jessica in 1 day = 1/20
Similarly,
∵ In 25 days the work is done by Karen = 1
∴ The work done by Karen in 1 day = 1/25
Similarly,
∵ In 30 days the work is done by Lisa = 1
∴ The work done by Lisa in 1 day = 1/30 part
Now, the work done by Jessica, Karen, and Lisa together in 1 day
= Jessica's 1 day work + Karen's 1 day work + Lisa's 1 day work
= 1/20 + 1/25 + 1/30
= 15 + 12 + 10/300
= 37/300 part of work
This means in 1 day, 37/300 part of work is done by Jessica, Karen and Lisa working together.
Now, the number of days required to finish 37/300 part of work by Jessica, Karen, and Lisa working together = 1
∴ the number of days required to finish the whole work (1 work) by Jessica + Karen + Lisa together
= 1/37/300
= 1 × 300/37 = 300/37 days
= 8 4/37 days = or 8.108 days
Thus, Jessica, Karen, and Lisa working together will finish the total work (1 work) in 8 4/37 days = or 8.108 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, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= a × b × c/ab + ac + bc days.
Here given,
The number of days required to finish the work by Jessica = 20 days
And the number of days required to finish the same work by Karen = 25 days
And the number of days required to finish the work by Lisa = 30 days
Thus, the number of days required to finish the work by Jessica, Karen, and Lisa together = ?
Here a = 20 days
And, b = 25 days
And, c = 30 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jessica, Karen, and Lisa working together
= 20 × 25 × 30/20 × 25 + 20 × 30 + 25 × 30 days
= 15000/500 + 600 + 750 days
= 15000/1850 days
= 15000/1850 days
= 15000 ÷ 50/1850 ÷ 50 = 300/37 days
= 8 4/37 days or 8.108
Thus, Jessica, Karen, and Lisa together will finish the work in 8 4/37 days or 8.108 days Answer
Similar Questions
(1) If Karen can finish the work in 24 days and Kevin can finish the same work in 29 days, then in how many days both can finish the work together?
(2) If Richard can finish the work in 14 days and Mark can finish the same work in 17 days, then in how many days both can finish the work together?
(3) Joseph can finish a work in 19 days. Charles can finish the same work in 24 days while Christopher can finish the work in 29 days. How long will it take to finish it if they work together?
(4) Gregory can finish a work in 89 days. Frank can finish the same work in 94 days while Patrick can finish the work in 99 days. How long will it take to finish it if they work together?
(5) If Robert can finish a work in 4 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working 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) 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?
(8) If Janet can finish the work in 98 days and Russell can finish the same work in 103 days, then in how many days both can finish the work together?
(9) If Rachel can finish the work in 94 days and Roy can finish the same work in 99 days, then in how many days both can finish the work together?
(10) If Ashley can finish the work in 36 days and Eric can finish the same work in 41 days, then in how many days both can finish the work together?