Question:
If Debra can finish the work in 92 days and Elijah can finish the same work in 97 days, then in how many days both can finish the work together?
Correct Answer
47 41/189 days or 47.217 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Debra = 92 days
And, the number of days to finish the same work by Elijah = 97 days
Thus, the number of days to finish the work by Debra and Elijah together = ?
Here,
∵ In 92 days the work done by Debra = 1
∴ In 1 day, the work done by Debra = 1/92 part
Similarly,
∵ In 97 days the work done by Elijah = 1
∴ In 1 day, the work done by Elijah = 1/97 part
Now, in 1 day, the work done by Debra and Elijah together
= In 1 day work done by Debra + In 1 day the work done by Elijah
= 1/92 + 1/97
= 97 + 92/8924
= 189/8924 part of work
This means in 1 day, 189/8924 part of work is done by Debra and Elijah working together.
Now, the number of days required to finish 189/8924 part of work by Debra + Elijah working together = 1
∴ the number of days required to finish 1 work by Debra + Elijah together
= 1/189/8924
= 1 × 8924/189 = 8924/189 days
= 47 41/189 days = or 47.217 days
Thus, Debra and Elijah working together will finish the work in 47 41/189 days = or 47.217 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 Debra = 92 days
And the number of days required to finish the same work by Elijah = 97 days
Thus, the number of days required to finish the work Debra and Elijah working together = ?
Here a = 92 days
And, b = 97 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Debra and Elijah working together
= 92 × 97/92 + 97 days
= 8924/189 days
= 47 41/189 days or 47.217
Thus, Debra and Elijah together will finish the work in 47 41/189 days or 47.217 days Answer
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