Question:
If Patricia can finish the work in 5 days and William can finish the same work in 9 days, then in how many days both can finish the work together?
Correct Answer
3 3/14 days or 3.214 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Patricia = 5 days
And, the number of days to finish the same work by William = 9 days
Thus, the number of days to finish the work by Patricia and William together = ?
Here,
∵ In 5 days the work done by Patricia = 1
∴ In 1 day, the work done by Patricia = 1/5 part
Similarly,
∵ In 9 days the work done by William = 1
∴ In 1 day, the work done by William = 1/9 part
Now, in 1 day, the work done by Patricia and William together
= In 1 day work done by Patricia + In 1 day the work done by William
= 1/5 + 1/9
= 9 + 5/45
= 14/45 part of work
This means in 1 day, 14/45 part of work is done by Patricia and William working together.
Now, the number of days required to finish 14/45 part of work by Patricia + William working together = 1
∴ the number of days required to finish 1 work by Patricia + William together
= 1/14/45
= 1 × 45/14 = 45/14 days
= 3 3/14 days = or 3.214 days
Thus, Patricia and William working together will finish the work in 3 3/14 days = or 3.214 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 Patricia = 5 days
And the number of days required to finish the same work by William = 9 days
Thus, the number of days required to finish the work Patricia and William working together = ?
Here a = 5 days
And, b = 9 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Patricia and William working together
= 5 × 9/5 + 9 days
= 45/14 days
= 3 3/14 days or 3.214
Thus, Patricia and William together will finish the work in 3 3/14 days or 3.214 days Answer
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