Question:
Donald can finish a work in 35 days. Paul can finish the same work in 40 days while Andrew can finish the work in 45 days. How long will it take to finish it if they work together?
Correct Answer
13 37/191 days or 13.194 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Donald = 35 days
And, the number of days required to finish the same work by Paul = 40 days
And, the number of days required to finish the same work by Andrew = 45 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 35 days the work is done by Donald = 1
∴ The work done by Donald in 1 day = 1/35
Similarly,
∵ In 40 days the work is done by Paul = 1
∴ The work done by Paul in 1 day = 1/40
Similarly,
∵ In 45 days the work is done by Andrew = 1
∴ The work done by Andrew in 1 day = 1/45 part
Now, the work done by Donald, Paul, and Andrew together in 1 day
= Donald's 1 day work + Paul's 1 day work + Andrew's 1 day work
= 1/35 + 1/40 + 1/45
= 72 + 63 + 56/2520
= 191/2520 part of work
This means in 1 day, 191/2520 part of work is done by Donald, Paul and Andrew working together.
Now, the number of days required to finish 191/2520 part of work by Donald, Paul, and Andrew working together = 1
∴ the number of days required to finish the whole work (1 work) by Donald + Paul + Andrew together
= 1/191/2520
= 1 × 2520/191 = 2520/191 days
= 13 37/191 days = or 13.194 days
Thus, Donald, Paul, and Andrew working together will finish the total work (1 work) in 13 37/191 days = or 13.194 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 Donald = 35 days
And the number of days required to finish the same work by Paul = 40 days
And the number of days required to finish the work by Andrew = 45 days
Thus, the number of days required to finish the work by Donald, Paul, and Andrew together = ?
Here a = 35 days
And, b = 40 days
And, c = 45 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Donald, Paul, and Andrew working together
= 35 × 40 × 45/35 × 40 + 35 × 45 + 40 × 45 days
= 63000/1400 + 1575 + 1800 days
= 63000/4775 days
= 63000/4775 days
= 63000 ÷ 25/4775 ÷ 25 = 2520/191 days
= 13 37/191 days or 13.194
Thus, Donald, Paul, and Andrew together will finish the work in 13 37/191 days or 13.194 days Answer
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