Question : If Donna can finish the work in 39 days and Brandon can finish the same work in 42 days, then in how many days both can finish the work together?
Correct Answer 20 2/9 days or 20.222 days
Solution & 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 = 42 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 42 days the work done by Brandon = 1
∴ In 1 day, the work done by Brandon = 1/42 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 + 1/42
= 14 + 13/546
= 27/546 part of work
= 27 ÷ 3/546 ÷ 3 part of work
= 9/182 part of work
This means, in 1 day, 9/182 part of the work is done by Donna and Brandon together.
Now, the number of days required to finish 9/182 part of work by Donna + Brandon working together = 1
∴ the number of days required to finish 1 work by Donna + Brandon together
= 1/9/182
= 1 × 182/9 = 182/9 days
= 20 2/9 days = or 20.222 days
Thus, Donna and Brandon working together will finish the work in 20 2/9 days = or 20.222 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 = 42 days
Thus, the number of days required to finish the work Donna and Brandon working together = ?
Here a = 39 days
And, b = 42 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 × 42/39 + 42 days
= 1638/81 days
= 1638 ÷ 9/81 ÷ 9 = 182/9 days
= 20 2/9 days or 20.222
Thus, Donna and Brandon together will finish the work in 20 2/9 days or 20.222 days Answer
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