Question:
If Robert can finish the work in 4 days and David can finish the same work in 7 days, then in how many days both can finish the work together?
Correct Answer
2 6/11 days or 2.545 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Robert = 4 days
And, the number of days to finish the same work by David = 7 days
Thus, the number of days to finish the work by Robert and David together = ?
Here,
∵ In 4 days the work done by Robert = 1
∴ In 1 day, the work done by Robert = 1/4 part
Similarly,
∵ In 7 days the work done by David = 1
∴ In 1 day, the work done by David = 1/7 part
Now, in 1 day, the work done by Robert and David together
= In 1 day work done by Robert + In 1 day the work done by David
= 1/4 + 1/7
= 7 + 4/28
= 11/28 part of work
This means in 1 day, 11/28 part of work is done by Robert and David working together.
Now, the number of days required to finish 11/28 part of work by Robert + David working together = 1
∴ the number of days required to finish 1 work by Robert + David together
= 1/11/28
= 1 × 28/11 = 28/11 days
= 2 6/11 days = or 2.545 days
Thus, Robert and David working together will finish the work in 2 6/11 days = or 2.545 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 Robert = 4 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 Robert and David working together = ?
Here a = 4 days
And, b = 7 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Robert and David working together
= 4 × 7/4 + 7 days
= 28/11 days
= 2 6/11 days or 2.545
Thus, Robert and David together will finish the work in 2 6/11 days or 2.545 days Answer
Similar Questions
(1) Sarah can finish a work in 22 days. Lisa can finish the same work in 27 days while Nancy can finish the work in 32 days. How long will it take to finish it if they work together?
(2) If Sandra can finish the work in 34 days and Gary can finish the same work in 39 days, then in how many days both can finish the work together?
(3) Jonathan can finish a work in 73 days. Larry can finish the same work in 78 days while Justin can finish the work in 83 days. How long will it take to finish it if they work together?
(4) 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?
(5) Angela can finish a work in 70 days. Anna can finish the same work in 75 days while Brenda can finish the work in 80 days. How long will it take to finish it if they work together?
(6) If Carolyn can finish the work in 96 days and Ralph can finish the same work in 101 days, then in how many days both can finish the work together?
(7) If Sandra can finish the work in 31 days and Gary can finish the same work in 35 days, then in how many days both can finish the work together?
(8) 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?
(9) Ronald can finish a work in 55 days. Jason can finish the same work in 60 days while Jeffrey can finish the work in 65 days. How long will it take to finish it if they work together?
(10) Catherine can finish a work in 100 days. Heather can finish the same work in 105 days while Diane can finish the work in 110 days. How long will it take to finish it if they work together?