Question:
If Laura can finish the work in 62 days and Kyle can finish the same work in 67 days, then in how many days both can finish the work together?
Correct Answer
32 26/129 days or 32.202 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Laura = 62 days
And, the number of days to finish the same work by Kyle = 67 days
Thus, the number of days to finish the work by Laura and Kyle together = ?
Here,
∵ In 62 days the work done by Laura = 1
∴ In 1 day, the work done by Laura = 1/62 part
Similarly,
∵ In 67 days the work done by Kyle = 1
∴ In 1 day, the work done by Kyle = 1/67 part
Now, in 1 day, the work done by Laura and Kyle together
= In 1 day work done by Laura + In 1 day the work done by Kyle
= 1/62 + 1/67
= 67 + 62/4154
= 129/4154 part of work
This means in 1 day, 129/4154 part of work is done by Laura and Kyle working together.
Now, the number of days required to finish 129/4154 part of work by Laura + Kyle working together = 1
∴ the number of days required to finish 1 work by Laura + Kyle together
= 1/129/4154
= 1 × 4154/129 = 4154/129 days
= 32 26/129 days = or 32.202 days
Thus, Laura and Kyle working together will finish the work in 32 26/129 days = or 32.202 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 Laura = 62 days
And the number of days required to finish the same work by Kyle = 67 days
Thus, the number of days required to finish the work Laura and Kyle working together = ?
Here a = 62 days
And, b = 67 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Laura and Kyle working together
= 62 × 67/62 + 67 days
= 4154/129 days
= 32 26/129 days or 32.202
Thus, Laura and Kyle together will finish the work in 32 26/129 days or 32.202 days Answer
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