Question:
If Katherine can finish the work in 88 days and Willie can finish the same work in 93 days, then in how many days both can finish the work together?
Correct Answer
45 39/181 days or 45.215 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Katherine = 88 days
And, the number of days to finish the same work by Willie = 93 days
Thus, the number of days to finish the work by Katherine and Willie together = ?
Here,
∵ In 88 days the work done by Katherine = 1
∴ In 1 day, the work done by Katherine = 1/88 part
Similarly,
∵ In 93 days the work done by Willie = 1
∴ In 1 day, the work done by Willie = 1/93 part
Now, in 1 day, the work done by Katherine and Willie together
= In 1 day work done by Katherine + In 1 day the work done by Willie
= 1/88 + 1/93
= 93 + 88/8184
= 181/8184 part of work
This means in 1 day, 181/8184 part of work is done by Katherine and Willie working together.
Now, the number of days required to finish 181/8184 part of work by Katherine + Willie working together = 1
∴ the number of days required to finish 1 work by Katherine + Willie together
= 1/181/8184
= 1 × 8184/181 = 8184/181 days
= 45 39/181 days = or 45.215 days
Thus, Katherine and Willie working together will finish the work in 45 39/181 days = or 45.215 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 Katherine = 88 days
And the number of days required to finish the same work by Willie = 93 days
Thus, the number of days required to finish the work Katherine and Willie working together = ?
Here a = 88 days
And, b = 93 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Katherine and Willie working together
= 88 × 93/88 + 93 days
= 8184/181 days
= 45 39/181 days or 45.215
Thus, Katherine and Willie together will finish the work in 45 39/181 days or 45.215 days Answer
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