Question:
John can finish a work in 5 days. Michael can finish the same work in 6 days while David can finish the work in 7 days. How long will it take to finish it if they work together?
Correct Answer
1 103/107 days or 1.963 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by John = 5 days
And, the number of days required to finish the same work by Michael = 6 days
And, the number of days required to finish the same work by David = 7 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 5 days the work is done by John = 1
∴ The work done by John in 1 day = 1/5
Similarly,
∵ In 6 days the work is done by Michael = 1
∴ The work done by Michael in 1 day = 1/6
Similarly,
∵ In 7 days the work is done by David = 1
∴ The work done by David in 1 day = 1/7 part
Now, the work done by John, Michael, and David together in 1 day
= John's 1 day work + Michael's 1 day work + David's 1 day work
= 1/5 + 1/6 + 1/7
= 42 + 35 + 30/210
= 107/210 part of work
This means in 1 day, 107/210 part of work is done by John, Michael and David working together.
Now, the number of days required to finish 107/210 part of work by John, Michael, and David working together = 1
∴ the number of days required to finish the whole work (1 work) by John + Michael + David together
= 1/107/210
= 1 × 210/107 = 210/107 days
= 1 103/107 days = or 1.963 days
Thus, John, Michael, and David working together will finish the total work (1 work) in 1 103/107 days = or 1.963 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 John = 5 days
And the number of days required to finish the same work by Michael = 6 days
And the number of days required to finish the work by David = 7 days
Thus, the number of days required to finish the work by John, Michael, and David together = ?
Here a = 5 days
And, b = 6 days
And, c = 7 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when John, Michael, and David working together
= 5 × 6 × 7/5 × 6 + 5 × 7 + 6 × 7 days
= 210/30 + 35 + 42 days
= 210/107 days
= 210/107 days
= 1 103/107 days or 1.963
Thus, John, Michael, and David together will finish the work in 1 103/107 days or 1.963 days Answer
Similar Questions
(1) If Carol can finish the work in 43 days and Alexander can finish the same work in 46 days, then in how many days both can finish the work together?
(2) If Steven can finish the work in 34 days and Jonathan can finish the same work in 37 days, then in how many days both can finish the work together?
(3) Paul can finish a work in 35 days. Andrew can finish the same work in 36 days while Joshua can finish the work in 37 days. How long will it take to finish it if they work together?
(4) 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?
(5) 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?
(6) Ashley can finish a work in 32 days. Kimberly can finish the same work in 33 days while Emily can finish the work in 34 days. How long will it take to finish it if they work together?
(7) Frank can finish a work in 93 days. Raymond can finish the same work in 98 days while Jack can finish the work in 103 days. How long will it take to finish it if they work together?
(8) If Elizabeth can finish the work in 33 days and Daniel can finish the same work in 49 days, then in how many days both can finish the work together?
(9) If Karen can finish the work in 21 days and Kevin can finish the same work in 25 days, then in how many days both can finish the work together?
(10) If Alexander can finish the work in 91 days and Wayne can finish the same work in 96 days, then in how many days both can finish the work together?