Question:
If Jennifer can finish the work in 7 days and Joseph can finish the same work in 10 days, then in how many days both can finish the work together?
Correct Answer
4 2/17 days or 4.118 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Jennifer = 7 days
And, the number of days to finish the same work by Joseph = 10 days
Thus, the number of days to finish the work by Jennifer and Joseph together = ?
Here,
∵ In 7 days the work done by Jennifer = 1
∴ In 1 day, the work done by Jennifer = 1/7 part
Similarly,
∵ In 10 days the work done by Joseph = 1
∴ In 1 day, the work done by Joseph = 1/10 part
Now, in 1 day, the work done by Jennifer and Joseph together
= In 1 day work done by Jennifer + In 1 day the work done by Joseph
= 1/7 + 1/10
= 10 + 7/70
= 17/70 part of work
This means in 1 day, 17/70 part of work is done by Jennifer and Joseph working together.
Now, the number of days required to finish 17/70 part of work by Jennifer + Joseph working together = 1
∴ the number of days required to finish 1 work by Jennifer + Joseph together
= 1/17/70
= 1 × 70/17 = 70/17 days
= 4 2/17 days = or 4.118 days
Thus, Jennifer and Joseph working together will finish the work in 4 2/17 days = or 4.118 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 Jennifer = 7 days
And the number of days required to finish the same work by Joseph = 10 days
Thus, the number of days required to finish the work Jennifer and Joseph working together = ?
Here a = 7 days
And, b = 10 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Jennifer and Joseph working together
= 7 × 10/7 + 10 days
= 70/17 days
= 4 2/17 days or 4.118
Thus, Jennifer and Joseph together will finish the work in 4 2/17 days or 4.118 days Answer
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