Question:
Sarah can finish a work in 18 days. Karen can finish the same work in 19 days while Lisa can finish the work in 20 days. How long will it take to finish it if they work together?
Correct Answer
6 174/541 days or 6.322 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Sarah = 18 days
And, the number of days required to finish the same work by Karen = 19 days
And, the number of days required to finish the same work by Lisa = 20 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 18 days the work is done by Sarah = 1
∴ The work done by Sarah in 1 day = 1/18
Similarly,
∵ In 19 days the work is done by Karen = 1
∴ The work done by Karen in 1 day = 1/19
Similarly,
∵ In 20 days the work is done by Lisa = 1
∴ The work done by Lisa in 1 day = 1/20 part
Now, the work done by Sarah, Karen, and Lisa together in 1 day
= Sarah's 1 day work + Karen's 1 day work + Lisa's 1 day work
= 1/18 + 1/19 + 1/20
= 190 + 180 + 171/3420
= 541/3420 part of work
This means in 1 day, 541/3420 part of work is done by Sarah, Karen and Lisa working together.
Now, the number of days required to finish 541/3420 part of work by Sarah, Karen, and Lisa working together = 1
∴ the number of days required to finish the whole work (1 work) by Sarah + Karen + Lisa together
= 1/541/3420
= 1 × 3420/541 = 3420/541 days
= 6 174/541 days = or 6.322 days
Thus, Sarah, Karen, and Lisa working together will finish the total work (1 work) in 6 174/541 days = or 6.322 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 Sarah = 18 days
And the number of days required to finish the same work by Karen = 19 days
And the number of days required to finish the work by Lisa = 20 days
Thus, the number of days required to finish the work by Sarah, Karen, and Lisa together = ?
Here a = 18 days
And, b = 19 days
And, c = 20 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Sarah, Karen, and Lisa working together
= 18 × 19 × 20/18 × 19 + 18 × 20 + 19 × 20 days
= 6840/342 + 360 + 380 days
= 6840/1082 days
= 6840/1082 days
= 6840 ÷ 2/1082 ÷ 2 = 3420/541 days
= 6 174/541 days or 6.322
Thus, Sarah, Karen, and Lisa together will finish the work in 6 174/541 days or 6.322 days Answer
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