Question:
If Shirley can finish the work in 72 days and Harold can finish the same work in 77 days, then in how many days both can finish the work together?
Correct Answer
37 31/149 days or 37.208 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Shirley = 72 days
And, the number of days to finish the same work by Harold = 77 days
Thus, the number of days to finish the work by Shirley and Harold together = ?
Here,
∵ In 72 days the work done by Shirley = 1
∴ In 1 day, the work done by Shirley = 1/72 part
Similarly,
∵ In 77 days the work done by Harold = 1
∴ In 1 day, the work done by Harold = 1/77 part
Now, in 1 day, the work done by Shirley and Harold together
= In 1 day work done by Shirley + In 1 day the work done by Harold
= 1/72 + 1/77
= 77 + 72/5544
= 149/5544 part of work
This means in 1 day, 149/5544 part of work is done by Shirley and Harold working together.
Now, the number of days required to finish 149/5544 part of work by Shirley + Harold working together = 1
∴ the number of days required to finish 1 work by Shirley + Harold together
= 1/149/5544
= 1 × 5544/149 = 5544/149 days
= 37 31/149 days = or 37.208 days
Thus, Shirley and Harold working together will finish the work in 37 31/149 days = or 37.208 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 Shirley = 72 days
And the number of days required to finish the same work by Harold = 77 days
Thus, the number of days required to finish the work Shirley and Harold working together = ?
Here a = 72 days
And, b = 77 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Shirley and Harold working together
= 72 × 77/72 + 77 days
= 5544/149 days
= 37 31/149 days or 37.208
Thus, Shirley and Harold together will finish the work in 37 31/149 days or 37.208 days Answer
Similar Questions
(1) Katherine can finish a work in 88 days. Debra can finish the same work in 93 days while Rachel can finish the work in 98 days. How long will it take to finish it if they work together?
(2) If Joseph can finish the work in 16 days and Steven can finish the same work in 20 days, then in how many days both can finish the work together?
(3) Patricia can finish a work in 8 days. Linda can finish the same work in 13 days while Elizabeth can finish the work in 18 days. How long will it take to finish it if they work together?
(4) Anthony can finish a work in 31 days. Donald can finish the same work in 36 days while Steven can finish the work in 41 days. How long will it take to finish it if they work together?
(5) 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?
(6) If Kevin can finish the work in 44 days and Frank can finish the same work in 47 days, then in how many days both can finish the work together?
(7) If Donna can finish the work in 42 days and Brandon can finish the same work in 47 days, then in how many days both can finish the work together?
(8) If William can finish the work in 34 days and Matthew can finish the same work in 50 days, then in how many days both can finish the work together?
(9) Michael can finish a work in 7 days. David can finish the same work in 8 days while William can finish the work in 9 days. How long will it take to finish it if they work together?
(10) Kimberly can finish a work in 38 days. Donna can finish the same work in 43 days while Michelle can finish the work in 48 days. How long will it take to finish it if they work together?