Question:
If John can finish the work in 6 days and Richard can finish the same work in 9 days, then in how many days both can finish the work together?
Correct Answer
3 3/5 days or 3.6 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by John = 6 days
And, the number of days to finish the same work by Richard = 9 days
Thus, the number of days to finish the work by John and Richard together = ?
Here,
∵ In 6 days the work done by John = 1
∴ In 1 day, the work done by John = 1/6 part
Similarly,
∵ In 9 days the work done by Richard = 1
∴ In 1 day, the work done by Richard = 1/9 part
Now, in 1 day, the work done by John and Richard together
= In 1 day work done by John + In 1 day the work done by Richard
= 1/6 + 1/9
= 3 + 2/18
= 5/18 part of work
This means in 1 day, 5/18 part of work is done by John and Richard working together.
Now, the number of days required to finish 5/18 part of work by John + Richard working together = 1
∴ the number of days required to finish 1 work by John + Richard together
= 1/5/18
= 1 × 18/5 = 18/5 days
= 3 3/5 days = or 3.6 days
Thus, John and Richard working together will finish the work in 3 3/5 days = or 3.6 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 John = 6 days
And the number of days required to finish the same work by Richard = 9 days
Thus, the number of days required to finish the work John and Richard working together = ?
Here a = 6 days
And, b = 9 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when John and Richard working together
= 6 × 9/6 + 9 days
= 54/15 days
= 54 ÷ 3/15 ÷ 3 = 18/5 days
= 3 3/5 days or 3.6
Thus, John and Richard together will finish the work in 3 3/5 days or 3.6 days Answer
Similar Questions
(1) If Barbara can finish the work in 13 days and Anthony can finish the same work in 16 days, then in how many days both can finish the work together?
(2) If Jennifer can finish the work in 7 days and Joseph can finish the same work in 11 days, then in how many days both can finish the work together?
(3) Alexander can finish a work in 91 days. Patrick can finish the same work in 96 days while Raymond can finish the work in 101 days. How long will it take to finish it if they work together?
(4) Kenneth can finish a work in 45 days. Brian can finish the same work in 50 days while George can finish the work in 55 days. How long will it take to finish it if they work together?
(5) If Daniel can finish the work in 24 days and Timothy can finish the same work in 28 days, then in how many days both can finish the work together?
(6) If Betty can finish the work in 30 days and Jason can finish the same work in 35 days, then in how many days both can finish the work together?
(7) If Michelle can finish the work in 41 days and Samuel can finish the same work in 44 days, then in how many days both can finish the work together?
(8) Steven can finish a work in 33 days. Paul can finish the same work in 34 days while Andrew can finish the work in 35 days. How long will it take to finish it if they work together?
(9) Rachel can finish a work in 94 days. Janet can finish the same work in 99 days while Catherine can finish the work in 104 days. How long will it take to finish it if they work together?
(10) If Andrew can finish the work in 38 days and Scott can finish the same work in 41 days, then in how many days both can finish the work together?