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
Similar Questions
(1) Donna can finish a work in 38 days. Michelle can finish the same work in 39 days while Carol can finish the work in 40 days. How long will it take to finish it if they work together?
(2) Melissa can finish a work in 48 days. Deborah can finish the same work in 49 days while Stephanie can finish the work in 50 days. How long will it take to finish it if they work together?
(3) If Patricia can finish the work in 27 days and William can finish the same work in 43 days, then in how many days both can finish the work together?
(4) If Gary can finish the work in 67 days and Christian can finish the same work in 72 days, then in how many days both can finish the work together?
(5) Margaret can finish a work in 28 days. Sandra can finish the same work in 29 days while Ashley can finish the work in 30 days. How long will it take to finish it if they work together?
(6) If Emily can finish the work in 40 days and Justin can finish the same work in 45 days, then in how many days both can finish the work together?
(7) Donald can finish a work in 35 days. Paul can finish the same work in 40 days while Andrew can finish the work in 45 days. How long will it take to finish it if they work together?
(8) If Carol can finish the work in 46 days and Alexander can finish the same work in 51 days, then in how many days both can finish the work together?
(9) Ronald can finish a work in 55 days. Jason can finish the same work in 60 days while Jeffrey can finish the work in 65 days. How long will it take to finish it if they work together?
(10) If Carol can finish the work in 43 days and Alexander can finish the same work in 47 days, then in how many days both can finish the work together?