Question : Mark can finish a work in 29 days. Donald can finish the same work in 30 days while Steven can finish the work in 31 days. How long will it take to finish it if they work together?
Correct Answer 9 2679/2699 days or 9.993 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Mark = 29 days
And, the number of days required to finish the same work by Donald = 30 days
And, the number of days required to finish the same work by Steven = 31 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 29 days the work is done by Mark = 1
∴ The work done by Mark in 1 day = 1/29
Similarly,
∵ In 30 days the work is done by Donald = 1
∴ The work done by Donald in 1 day = 1/30
Similarly,
∵ In 31 days the work is done by Steven = 1
∴ The work done by Steven in 1 day = 1/31 part
Now, the work done by Mark, Donald, and Steven together in 1 day
= Mark's 1 day work + Donald's 1 day work + Steven's 1 day work
= 1/29 + 1/30 + 1/31
= 930 + 899 + 870/26970
= 2699/26970 part of work
This means in 1 day, 2699/26970 part of work is done by Mark, Donald and Steven working together.
Now, the number of days required to finish 2699/26970 part of work by Mark, Donald, and Steven working together = 1
∴ the number of days required to finish the whole work (1 work) by Mark + Donald + Steven together
= 1/2699/26970
= 1 × 26970/2699 = 26970/2699 days
= 9 2679/2699 days = or 9.993 days
Thus, Mark, Donald, and Steven working together will finish the total work (1 work) in 9 2679/2699 days = or 9.993 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 Mark = 29 days
And the number of days required to finish the same work by Donald = 30 days
And the number of days required to finish the work by Steven = 31 days
Thus, the number of days required to finish the work by Mark, Donald, and Steven together = ?
Here a = 29 days
And, b = 30 days
And, c = 31 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Mark, Donald, and Steven working together
= 29 × 30 × 31/29 × 30 + 29 × 31 + 30 × 31 days
= 26970/870 + 899 + 930 days
= 26970/2699 days
= 26970/2699 days
= 9 2679/2699 days or 9.993
Thus, Mark, Donald, and Steven together will finish the work in 9 2679/2699 days or 9.993 days Answer
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