Question:
If Michelle can finish the work in 41 days and Samuel can finish the same work in 45 days, then in how many days both can finish the work together?
Correct Answer
21 39/86 days or 21.453 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Michelle = 41 days
And, the number of days to finish the same work by Samuel = 45 days
Thus, the number of days to finish the work by Michelle and Samuel together = ?
Here,
∵ In 41 days the work done by Michelle = 1
∴ In 1 day, the work done by Michelle = 1/41 part
Similarly,
∵ In 45 days the work done by Samuel = 1
∴ In 1 day, the work done by Samuel = 1/45 part
Now, in 1 day, the work done by Michelle and Samuel together
= In 1 day work done by Michelle + In 1 day the work done by Samuel
= 1/41 + 1/45
= 45 + 41/1845
= 86/1845 part of work
This means in 1 day, 86/1845 part of work is done by Michelle and Samuel working together.
Now, the number of days required to finish 86/1845 part of work by Michelle + Samuel working together = 1
∴ the number of days required to finish 1 work by Michelle + Samuel together
= 1/86/1845
= 1 × 1845/86 = 1845/86 days
= 21 39/86 days = or 21.453 days
Thus, Michelle and Samuel working together will finish the work in 21 39/86 days = or 21.453 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 Michelle = 41 days
And the number of days required to finish the same work by Samuel = 45 days
Thus, the number of days required to finish the work Michelle and Samuel working together = ?
Here a = 41 days
And, b = 45 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Michelle and Samuel working together
= 41 × 45/41 + 45 days
= 1845/86 days
= 21 39/86 days or 21.453
Thus, Michelle and Samuel together will finish the work in 21 39/86 days or 21.453 days Answer
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