Question:
If Kathleen can finish the work in 66 days and Jeremy can finish the same work in 71 days, then in how many days both can finish the work together?
Correct Answer
34 28/137 days or 34.204 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Kathleen = 66 days
And, the number of days to finish the same work by Jeremy = 71 days
Thus, the number of days to finish the work by Kathleen and Jeremy together = ?
Here,
∵ In 66 days the work done by Kathleen = 1
∴ In 1 day, the work done by Kathleen = 1/66 part
Similarly,
∵ In 71 days the work done by Jeremy = 1
∴ In 1 day, the work done by Jeremy = 1/71 part
Now, in 1 day, the work done by Kathleen and Jeremy together
= In 1 day work done by Kathleen + In 1 day the work done by Jeremy
= 1/66 + 1/71
= 71 + 66/4686
= 137/4686 part of work
This means in 1 day, 137/4686 part of work is done by Kathleen and Jeremy working together.
Now, the number of days required to finish 137/4686 part of work by Kathleen + Jeremy working together = 1
∴ the number of days required to finish 1 work by Kathleen + Jeremy together
= 1/137/4686
= 1 × 4686/137 = 4686/137 days
= 34 28/137 days = or 34.204 days
Thus, Kathleen and Jeremy working together will finish the work in 34 28/137 days = or 34.204 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 Kathleen = 66 days
And the number of days required to finish the same work by Jeremy = 71 days
Thus, the number of days required to finish the work Kathleen and Jeremy working together = ?
Here a = 66 days
And, b = 71 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Kathleen and Jeremy working together
= 66 × 71/66 + 71 days
= 4686/137 days
= 34 28/137 days or 34.204
Thus, Kathleen and Jeremy together will finish the work in 34 28/137 days or 34.204 days Answer
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