Question:
If Brandon can finish the work in 83 days and Joe can finish the same work in 88 days, then in how many days both can finish the work together?
Correct Answer
42 122/171 days or 42.713 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Brandon = 83 days
And, the number of days to finish the same work by Joe = 88 days
Thus, the number of days to finish the work by Brandon and Joe together = ?
Here,
∵ In 83 days the work done by Brandon = 1
∴ In 1 day, the work done by Brandon = 1/83 part
Similarly,
∵ In 88 days the work done by Joe = 1
∴ In 1 day, the work done by Joe = 1/88 part
Now, in 1 day, the work done by Brandon and Joe together
= In 1 day work done by Brandon + In 1 day the work done by Joe
= 1/83 + 1/88
= 88 + 83/7304
= 171/7304 part of work
This means in 1 day, 171/7304 part of work is done by Brandon and Joe working together.
Now, the number of days required to finish 171/7304 part of work by Brandon + Joe working together = 1
∴ the number of days required to finish 1 work by Brandon + Joe together
= 1/171/7304
= 1 × 7304/171 = 7304/171 days
= 42 122/171 days = or 42.713 days
Thus, Brandon and Joe working together will finish the work in 42 122/171 days = or 42.713 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 Brandon = 83 days
And the number of days required to finish the same work by Joe = 88 days
Thus, the number of days required to finish the work Brandon and Joe working together = ?
Here a = 83 days
And, b = 88 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Brandon and Joe working together
= 83 × 88/83 + 88 days
= 7304/171 days
= 42 122/171 days or 42.713
Thus, Brandon and Joe together will finish the work in 42 122/171 days or 42.713 days Answer
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