Question : If Kimberly can finish the work in 35 days and Stephen can finish the same work in 38 days, then in how many days both can finish the work together?
Correct Answer 18 16/73 days or 18.219 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Kimberly = 35 days
And, the number of days to finish the same work by Stephen = 38 days
Thus, the number of days to finish the work by Kimberly and Stephen together = ?
Here,
∵ In 35 days the work done by Kimberly = 1
∴ In 1 day, the work done by Kimberly = 1/35 part
Similarly,
∵ In 38 days the work done by Stephen = 1
∴ In 1 day, the work done by Stephen = 1/38 part
Now, in 1 day, the work done by Kimberly and Stephen together
= In 1 day work done by Kimberly + In 1 day the work done by Stephen
= 1/35 + 1/38
= 38 + 35/1330
= 73/1330 part of work
This means in 1 day, 73/1330 part of work is done by Kimberly and Stephen working together.
Now, the number of days required to finish 73/1330 part of work by Kimberly + Stephen working together = 1
∴ the number of days required to finish 1 work by Kimberly + Stephen together
= 1/73/1330
= 1 × 1330/73 = 1330/73 days
= 18 16/73 days = or 18.219 days
Thus, Kimberly and Stephen working together will finish the work in 18 16/73 days = or 18.219 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 Kimberly = 35 days
And the number of days required to finish the same work by Stephen = 38 days
Thus, the number of days required to finish the work Kimberly and Stephen working together = ?
Here a = 35 days
And, b = 38 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Kimberly and Stephen working together
= 35 × 38/35 + 38 days
= 1330/73 days
= 18 16/73 days or 18.219
Thus, Kimberly and Stephen together will finish the work in 18 16/73 days or 18.219 days Answer
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