Question:
Janet can finish a work in 98 days. Maria can finish the same work in 103 days while Heather can finish the work in 108 days. How long will it take to finish it if they work together?
Correct Answer
34 4442/15901 days or 34.279 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Janet = 98 days
And, the number of days required to finish the same work by Maria = 103 days
And, the number of days required to finish the same work by Heather = 108 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 98 days the work is done by Janet = 1
∴ The work done by Janet in 1 day = 1/98
Similarly,
∵ In 103 days the work is done by Maria = 1
∴ The work done by Maria in 1 day = 1/103
Similarly,
∵ In 108 days the work is done by Heather = 1
∴ The work done by Heather in 1 day = 1/108 part
Now, the work done by Janet, Maria, and Heather together in 1 day
= Janet's 1 day work + Maria's 1 day work + Heather's 1 day work
= 1/98 + 1/103 + 1/108
= 5562 + 5292 + 5047/545076
= 15901/545076 part of work
This means in 1 day, 15901/545076 part of work is done by Janet, Maria and Heather working together.
Now, the number of days required to finish 15901/545076 part of work by Janet, Maria, and Heather working together = 1
∴ the number of days required to finish the whole work (1 work) by Janet + Maria + Heather together
= 1/15901/545076
= 1 × 545076/15901 = 545076/15901 days
= 34 4442/15901 days = or 34.279 days
Thus, Janet, Maria, and Heather working together will finish the total work (1 work) in 34 4442/15901 days = or 34.279 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 Janet = 98 days
And the number of days required to finish the same work by Maria = 103 days
And the number of days required to finish the work by Heather = 108 days
Thus, the number of days required to finish the work by Janet, Maria, and Heather together = ?
Here a = 98 days
And, b = 103 days
And, c = 108 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Janet, Maria, and Heather working together
= 98 × 103 × 108/98 × 103 + 98 × 108 + 103 × 108 days
= 1090152/10094 + 10584 + 11124 days
= 1090152/31802 days
= 1090152/31802 days
= 1090152 ÷ 2/31802 ÷ 2 = 545076/15901 days
= 34 4442/15901 days or 34.279
Thus, Janet, Maria, and Heather together will finish the work in 34 4442/15901 days or 34.279 days Answer
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