Question:
If Donna can finish the work in 39 days and Brandon can finish the same work in 43 days, then in how many days both can finish the work together?
Correct Answer
20 37/82 days or 20.451 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Donna = 39 days
And, the number of days to finish the same work by Brandon = 43 days
Thus, the number of days to finish the work by Donna and Brandon together = ?
Here,
∵ In 39 days the work done by Donna = 1
∴ In 1 day, the work done by Donna = 1/39 part
Similarly,
∵ In 43 days the work done by Brandon = 1
∴ In 1 day, the work done by Brandon = 1/43 part
Now, in 1 day, the work done by Donna and Brandon together
= In 1 day work done by Donna + In 1 day the work done by Brandon
= 1/39 + 1/43
= 43 + 39/1677
= 82/1677 part of work
This means in 1 day, 82/1677 part of work is done by Donna and Brandon working together.
Now, the number of days required to finish 82/1677 part of work by Donna + Brandon working together = 1
∴ the number of days required to finish 1 work by Donna + Brandon together
= 1/82/1677
= 1 × 1677/82 = 1677/82 days
= 20 37/82 days = or 20.451 days
Thus, Donna and Brandon working together will finish the work in 20 37/82 days = or 20.451 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 Donna = 39 days
And the number of days required to finish the same work by Brandon = 43 days
Thus, the number of days required to finish the work Donna and Brandon working together = ?
Here a = 39 days
And, b = 43 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Donna and Brandon working together
= 39 × 43/39 + 43 days
= 1677/82 days
= 20 37/82 days or 20.451
Thus, Donna and Brandon together will finish the work in 20 37/82 days or 20.451 days Answer
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