Question:
If Amanda can finish the work in 45 days and Patrick can finish the same work in 49 days, then in how many days both can finish the work together?
Correct Answer
23 43/94 days or 23.457 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Amanda = 45 days
And, the number of days to finish the same work by Patrick = 49 days
Thus, the number of days to finish the work by Amanda and Patrick together = ?
Here,
∵ In 45 days the work done by Amanda = 1
∴ In 1 day, the work done by Amanda = 1/45 part
Similarly,
∵ In 49 days the work done by Patrick = 1
∴ In 1 day, the work done by Patrick = 1/49 part
Now, in 1 day, the work done by Amanda and Patrick together
= In 1 day work done by Amanda + In 1 day the work done by Patrick
= 1/45 + 1/49
= 49 + 45/2205
= 94/2205 part of work
This means in 1 day, 94/2205 part of work is done by Amanda and Patrick working together.
Now, the number of days required to finish 94/2205 part of work by Amanda + Patrick working together = 1
∴ the number of days required to finish 1 work by Amanda + Patrick together
= 1/94/2205
= 1 × 2205/94 = 2205/94 days
= 23 43/94 days = or 23.457 days
Thus, Amanda and Patrick working together will finish the work in 23 43/94 days = or 23.457 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 Amanda = 45 days
And the number of days required to finish the same work by Patrick = 49 days
Thus, the number of days required to finish the work Amanda and Patrick working together = ?
Here a = 45 days
And, b = 49 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Amanda and Patrick working together
= 45 × 49/45 + 49 days
= 2205/94 days
= 23 43/94 days or 23.457
Thus, Amanda and Patrick together will finish the work in 23 43/94 days or 23.457 days Answer
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