Question : Debra can finish a work in 92 days. Carolyn can finish the same work in 97 days while Janet can finish the work in 102 days. How long will it take to finish it if they work together?
Correct Answer 32 3892/14101 days or 32.276 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Debra = 92 days
And, the number of days required to finish the same work by Carolyn = 97 days
And, the number of days required to finish the same work by Janet = 102 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 92 days the work is done by Debra = 1
∴ The work done by Debra in 1 day = 1/92
Similarly,
∵ In 97 days the work is done by Carolyn = 1
∴ The work done by Carolyn in 1 day = 1/97
Similarly,
∵ In 102 days the work is done by Janet = 1
∴ The work done by Janet in 1 day = 1/102 part
Now, the work done by Debra, Carolyn, and Janet together in 1 day
= Debra's 1 day work + Carolyn's 1 day work + Janet's 1 day work
= 1/92 + 1/97 + 1/102
= 4947 + 4692 + 4462/455124
= 14101/455124 part of work
This means in 1 day, 14101/455124 part of work is done by Debra, Carolyn and Janet working together.
Now, the number of days required to finish 14101/455124 part of work by Debra, Carolyn, and Janet working together = 1
∴ the number of days required to finish the whole work (1 work) by Debra + Carolyn + Janet together
= 1/14101/455124
= 1 × 455124/14101 = 455124/14101 days
= 32 3892/14101 days = or 32.276 days
Thus, Debra, Carolyn, and Janet working together will finish the total work (1 work) in 32 3892/14101 days = or 32.276 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 Debra = 92 days
And the number of days required to finish the same work by Carolyn = 97 days
And the number of days required to finish the work by Janet = 102 days
Thus, the number of days required to finish the work by Debra, Carolyn, and Janet together = ?
Here a = 92 days
And, b = 97 days
And, c = 102 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Debra, Carolyn, and Janet working together
= 92 × 97 × 102/92 × 97 + 92 × 102 + 97 × 102 days
= 910248/8924 + 9384 + 9894 days
= 910248/28202 days
= 910248/28202 days
= 910248 ÷ 2/28202 ÷ 2 = 455124/14101 days
= 32 3892/14101 days or 32.276
Thus, Debra, Carolyn, and Janet together will finish the work in 32 3892/14101 days or 32.276 days Answer
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