Question:
If Stephanie can finish the work in 56 days and Adam can finish the same work in 61 days, then in how many days both can finish the work together?
Correct Answer
29 23/117 days or 29.197 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Stephanie = 56 days
And, the number of days to finish the same work by Adam = 61 days
Thus, the number of days to finish the work by Stephanie and Adam together = ?
Here,
∵ In 56 days the work done by Stephanie = 1
∴ In 1 day, the work done by Stephanie = 1/56 part
Similarly,
∵ In 61 days the work done by Adam = 1
∴ In 1 day, the work done by Adam = 1/61 part
Now, in 1 day, the work done by Stephanie and Adam together
= In 1 day work done by Stephanie + In 1 day the work done by Adam
= 1/56 + 1/61
= 61 + 56/3416
= 117/3416 part of work
This means in 1 day, 117/3416 part of work is done by Stephanie and Adam working together.
Now, the number of days required to finish 117/3416 part of work by Stephanie + Adam working together = 1
∴ the number of days required to finish 1 work by Stephanie + Adam together
= 1/117/3416
= 1 × 3416/117 = 3416/117 days
= 29 23/117 days = or 29.197 days
Thus, Stephanie and Adam working together will finish the work in 29 23/117 days = or 29.197 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 Stephanie = 56 days
And the number of days required to finish the same work by Adam = 61 days
Thus, the number of days required to finish the work Stephanie and Adam working together = ?
Here a = 56 days
And, b = 61 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Stephanie and Adam working together
= 56 × 61/56 + 61 days
= 3416/117 days
= 29 23/117 days or 29.197
Thus, Stephanie and Adam together will finish the work in 29 23/117 days or 29.197 days Answer
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