Question:
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?
Correct Answer
17 51/71 days or 17.718 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Steven = 34 days
And, the number of days to finish the same work by Jonathan = 37 days
Thus, the number of days to finish the work by Steven and Jonathan together = ?
Here,
∵ In 34 days the work done by Steven = 1
∴ In 1 day, the work done by Steven = 1/34 part
Similarly,
∵ In 37 days the work done by Jonathan = 1
∴ In 1 day, the work done by Jonathan = 1/37 part
Now, in 1 day, the work done by Steven and Jonathan together
= In 1 day work done by Steven + In 1 day the work done by Jonathan
= 1/34 + 1/37
= 37 + 34/1258
= 71/1258 part of work
This means in 1 day, 71/1258 part of work is done by Steven and Jonathan working together.
Now, the number of days required to finish 71/1258 part of work by Steven + Jonathan working together = 1
∴ the number of days required to finish 1 work by Steven + Jonathan together
= 1/71/1258
= 1 × 1258/71 = 1258/71 days
= 17 51/71 days = or 17.718 days
Thus, Steven and Jonathan working together will finish the work in 17 51/71 days = or 17.718 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 Steven = 34 days
And the number of days required to finish the same work by Jonathan = 37 days
Thus, the number of days required to finish the work Steven and Jonathan working together = ?
Here a = 34 days
And, b = 37 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Steven and Jonathan working together
= 34 × 37/34 + 37 days
= 1258/71 days
= 17 51/71 days or 17.718
Thus, Steven and Jonathan together will finish the work in 17 51/71 days or 17.718 days Answer
Similar Questions
(1) If Anthony can finish the work in 31 days and Jeffrey can finish the same work in 36 days, then in how many days both can finish the work together?
(2) Susan can finish a work in 14 days. Jessica can finish the same work in 15 days while Sarah can finish the work in 16 days. How long will it take to finish it if they work together?
(3) 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?
(4) Margaret can finish a work in 28 days. Sandra can finish the same work in 29 days while Ashley can finish the work in 30 days. How long will it take to finish it if they work together?
(5) If Debra can finish the work in 92 days and Elijah can finish the same work in 97 days, then in how many days both can finish the work together?
(6) Amy can finish a work in 68 days. Shirley can finish the same work in 73 days while Anna can finish the work in 78 days. How long will it take to finish it if they work together?
(7) 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?
(8) Donna can finish a work in 42 days. Carol can finish the same work in 47 days while Amanda can finish the work in 52 days. How long will it take to finish it if they work together?
(9) Debra can finish a work in 92 days. Carolyn can finish the same work in 97 days while Janet can finish the work in 102 days. How long will it take to finish it if they work together?
(10) If Emily can finish the work in 40 days and Justin can finish the same work in 45 days, then in how many days both can finish the work together?