Question:
If Emily can finish the work in 37 days and Justin can finish the same work in 41 days, then in how many days both can finish the work together?
Correct Answer
19 35/78 days or 19.449 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Emily = 37 days
And, the number of days to finish the same work by Justin = 41 days
Thus, the number of days to finish the work by Emily and Justin together = ?
Here,
∵ In 37 days the work done by Emily = 1
∴ In 1 day, the work done by Emily = 1/37 part
Similarly,
∵ In 41 days the work done by Justin = 1
∴ In 1 day, the work done by Justin = 1/41 part
Now, in 1 day, the work done by Emily and Justin together
= In 1 day work done by Emily + In 1 day the work done by Justin
= 1/37 + 1/41
= 41 + 37/1517
= 78/1517 part of work
This means in 1 day, 78/1517 part of work is done by Emily and Justin working together.
Now, the number of days required to finish 78/1517 part of work by Emily + Justin working together = 1
∴ the number of days required to finish 1 work by Emily + Justin together
= 1/78/1517
= 1 × 1517/78 = 1517/78 days
= 19 35/78 days = or 19.449 days
Thus, Emily and Justin working together will finish the work in 19 35/78 days = or 19.449 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 Emily = 37 days
And the number of days required to finish the same work by Justin = 41 days
Thus, the number of days required to finish the work Emily and Justin working together = ?
Here a = 37 days
And, b = 41 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Emily and Justin working together
= 37 × 41/37 + 41 days
= 1517/78 days
= 19 35/78 days or 19.449
Thus, Emily and Justin together will finish the work in 19 35/78 days or 19.449 days Answer
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