Question:
If Samantha can finish the work in 86 days and Logan can finish the same work in 91 days, then in how many days both can finish the work together?
Correct Answer
44 38/177 days or 44.215 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Samantha = 86 days
And, the number of days to finish the same work by Logan = 91 days
Thus, the number of days to finish the work by Samantha and Logan together = ?
Here,
∵ In 86 days the work done by Samantha = 1
∴ In 1 day, the work done by Samantha = 1/86 part
Similarly,
∵ In 91 days the work done by Logan = 1
∴ In 1 day, the work done by Logan = 1/91 part
Now, in 1 day, the work done by Samantha and Logan together
= In 1 day work done by Samantha + In 1 day the work done by Logan
= 1/86 + 1/91
= 91 + 86/7826
= 177/7826 part of work
This means in 1 day, 177/7826 part of work is done by Samantha and Logan working together.
Now, the number of days required to finish 177/7826 part of work by Samantha + Logan working together = 1
∴ the number of days required to finish 1 work by Samantha + Logan together
= 1/177/7826
= 1 × 7826/177 = 7826/177 days
= 44 38/177 days = or 44.215 days
Thus, Samantha and Logan working together will finish the work in 44 38/177 days = or 44.215 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 Samantha = 86 days
And the number of days required to finish the same work by Logan = 91 days
Thus, the number of days required to finish the work Samantha and Logan working together = ?
Here a = 86 days
And, b = 91 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Samantha and Logan working together
= 86 × 91/86 + 91 days
= 7826/177 days
= 44 38/177 days or 44.215
Thus, Samantha and Logan together will finish the work in 44 38/177 days or 44.215 days Answer
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