Question:
If Emma can finish the work in 80 days and Jordan can finish the same work in 85 days, then in how many days both can finish the work together?
Correct Answer
41 7/33 days or 41.212 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Emma = 80 days
And, the number of days to finish the same work by Jordan = 85 days
Thus, the number of days to finish the work by Emma and Jordan together = ?
Here,
∵ In 80 days the work done by Emma = 1
∴ In 1 day, the work done by Emma = 1/80 part
Similarly,
∵ In 85 days the work done by Jordan = 1
∴ In 1 day, the work done by Jordan = 1/85 part
Now, in 1 day, the work done by Emma and Jordan together
= In 1 day work done by Emma + In 1 day the work done by Jordan
= 1/80 + 1/85
= 17 + 16/1360
= 33/1360 part of work
This means in 1 day, 33/1360 part of work is done by Emma and Jordan working together.
Now, the number of days required to finish 33/1360 part of work by Emma + Jordan working together = 1
∴ the number of days required to finish 1 work by Emma + Jordan together
= 1/33/1360
= 1 × 1360/33 = 1360/33 days
= 41 7/33 days = or 41.212 days
Thus, Emma and Jordan working together will finish the work in 41 7/33 days = or 41.212 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 Emma = 80 days
And the number of days required to finish the same work by Jordan = 85 days
Thus, the number of days required to finish the work Emma and Jordan working together = ?
Here a = 80 days
And, b = 85 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Emma and Jordan working together
= 80 × 85/80 + 85 days
= 6800/165 days
= 6800 ÷ 5/165 ÷ 5 = 1360/33 days
= 41 7/33 days or 41.212
Thus, Emma and Jordan together will finish the work in 41 7/33 days or 41.212 days Answer
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