Question : Matthew can finish a work in 29 days. Mark can finish the same work in 34 days while Donald can finish the work in 39 days. How long will it take to finish it if they work together?
Correct Answer 11 581/3443 days or 11.169 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Matthew = 29 days
And, the number of days required to finish the same work by Mark = 34 days
And, the number of days required to finish the same work by Donald = 39 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 Matthew = 1
∴ The work done by Matthew in 1 day = 1/29
Similarly,
∵ In 34 days the work is done by Mark = 1
∴ The work done by Mark in 1 day = 1/34
Similarly,
∵ In 39 days the work is done by Donald = 1
∴ The work done by Donald in 1 day = 1/39 part
Now, the work done by Matthew, Mark, and Donald together in 1 day
= Matthew's 1 day work + Mark's 1 day work + Donald's 1 day work
= 1/29 + 1/34 + 1/39
= 1326 + 1131 + 986/38454
= 3443/38454 part of work
This means in 1 day, 3443/38454 part of work is done by Matthew, Mark and Donald working together.
Now, the number of days required to finish 3443/38454 part of work by Matthew, Mark, and Donald working together = 1
∴ the number of days required to finish the whole work (1 work) by Matthew + Mark + Donald together
= 1/3443/38454
= 1 × 38454/3443 = 38454/3443 days
= 11 581/3443 days = or 11.169 days
Thus, Matthew, Mark, and Donald working together will finish the total work (1 work) in 11 581/3443 days = or 11.169 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 Matthew = 29 days
And the number of days required to finish the same work by Mark = 34 days
And the number of days required to finish the work by Donald = 39 days
Thus, the number of days required to finish the work by Matthew, Mark, and Donald together = ?
Here a = 29 days
And, b = 34 days
And, c = 39 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Matthew, Mark, and Donald working together
= 29 × 34 × 39/29 × 34 + 29 × 39 + 34 × 39 days
= 38454/986 + 1131 + 1326 days
= 38454/3443 days
= 38454/3443 days
= 11 581/3443 days or 11.169
Thus, Matthew, Mark, and Donald together will finish the work in 11 581/3443 days or 11.169 days Answer
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