Question : Betty can finish a work in 30 days. Sandra can finish the same work in 35 days while Ashley can finish the work in 40 days. How long will it take to finish it if they work together?
Correct Answer 11 37/73 days or 11.507 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Betty = 30 days
And, the number of days required to finish the same work by Sandra = 35 days
And, the number of days required to finish the same work by Ashley = 40 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 30 days the work is done by Betty = 1
∴ The work done by Betty in 1 day = 1/30
Similarly,
∵ In 35 days the work is done by Sandra = 1
∴ The work done by Sandra in 1 day = 1/35
Similarly,
∵ In 40 days the work is done by Ashley = 1
∴ The work done by Ashley in 1 day = 1/40 part
Now, the work done by Betty, Sandra, and Ashley together in 1 day
= Betty's 1 day work + Sandra's 1 day work + Ashley's 1 day work
= 1/30 + 1/35 + 1/40
= 28 + 24 + 21/840
= 73/840 part of work
This means in 1 day, 73/840 part of work is done by Betty, Sandra and Ashley working together.
Now, the number of days required to finish 73/840 part of work by Betty, Sandra, and Ashley working together = 1
∴ the number of days required to finish the whole work (1 work) by Betty + Sandra + Ashley together
= 1/73/840
= 1 × 840/73 = 840/73 days
= 11 37/73 days = or 11.507 days
Thus, Betty, Sandra, and Ashley working together will finish the total work (1 work) in 11 37/73 days = or 11.507 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 Betty = 30 days
And the number of days required to finish the same work by Sandra = 35 days
And the number of days required to finish the work by Ashley = 40 days
Thus, the number of days required to finish the work by Betty, Sandra, and Ashley together = ?
Here a = 30 days
And, b = 35 days
And, c = 40 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Betty, Sandra, and Ashley working together
= 30 × 35 × 40/30 × 35 + 30 × 40 + 35 × 40 days
= 42000/1050 + 1200 + 1400 days
= 42000/3650 days
= 42000/3650 days
= 42000 ÷ 50/3650 ÷ 50 = 840/73 days
= 11 37/73 days or 11.507
Thus, Betty, Sandra, and Ashley together will finish the work in 11 37/73 days or 11.507 days Answer
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