Question : Emily can finish a work in 40 days. Michelle can finish the same work in 45 days while Carol can finish the work in 50 days. How long will it take to finish it if they work together?
Correct Answer 14 106/121 days or 14.876 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Emily = 40 days
And, the number of days required to finish the same work by Michelle = 45 days
And, the number of days required to finish the same work by Carol = 50 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 40 days the work is done by Emily = 1
∴ The work done by Emily in 1 day = 1/40
Similarly,
∵ In 45 days the work is done by Michelle = 1
∴ The work done by Michelle in 1 day = 1/45
Similarly,
∵ In 50 days the work is done by Carol = 1
∴ The work done by Carol in 1 day = 1/50 part
Now, the work done by Emily, Michelle, and Carol together in 1 day
= Emily's 1 day work + Michelle's 1 day work + Carol's 1 day work
= 1/40 + 1/45 + 1/50
= 45 + 40 + 36/1800
= 121/1800 part of work
This means in 1 day, 121/1800 part of work is done by Emily, Michelle and Carol working together.
Now, the number of days required to finish 121/1800 part of work by Emily, Michelle, and Carol working together = 1
∴ the number of days required to finish the whole work (1 work) by Emily + Michelle + Carol together
= 1/121/1800
= 1 × 1800/121 = 1800/121 days
= 14 106/121 days = or 14.876 days
Thus, Emily, Michelle, and Carol working together will finish the total work (1 work) in 14 106/121 days = or 14.876 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, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= a × b × c/ab + ac + bc days.
Here given,
The number of days required to finish the work by Emily = 40 days
And the number of days required to finish the same work by Michelle = 45 days
And the number of days required to finish the work by Carol = 50 days
Thus, the number of days required to finish the work by Emily, Michelle, and Carol together = ?
Here a = 40 days
And, b = 45 days
And, c = 50 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Emily, Michelle, and Carol working together
= 40 × 45 × 50/40 × 45 + 40 × 50 + 45 × 50 days
= 90000/1800 + 2000 + 2250 days
= 90000/6050 days
= 90000/6050 days
= 90000 ÷ 50/6050 ÷ 50 = 1800/121 days
= 14 106/121 days or 14.876
Thus, Emily, Michelle, and Carol together will finish the work in 14 106/121 days or 14.876 days Answer
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