Question:
Stephen can finish a work in 75 days. Justin can finish the same work in 80 days while Scott can finish the work in 85 days. How long will it take to finish it if they work together?
Correct Answer
26 458/767 days or 26.597 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Stephen = 75 days
And, the number of days required to finish the same work by Justin = 80 days
And, the number of days required to finish the same work by Scott = 85 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 75 days the work is done by Stephen = 1
∴ The work done by Stephen in 1 day = 1/75
Similarly,
∵ In 80 days the work is done by Justin = 1
∴ The work done by Justin in 1 day = 1/80
Similarly,
∵ In 85 days the work is done by Scott = 1
∴ The work done by Scott in 1 day = 1/85 part
Now, the work done by Stephen, Justin, and Scott together in 1 day
= Stephen's 1 day work + Justin's 1 day work + Scott's 1 day work
= 1/75 + 1/80 + 1/85
= 272 + 255 + 240/20400
= 767/20400 part of work
This means in 1 day, 767/20400 part of work is done by Stephen, Justin and Scott working together.
Now, the number of days required to finish 767/20400 part of work by Stephen, Justin, and Scott working together = 1
∴ the number of days required to finish the whole work (1 work) by Stephen + Justin + Scott together
= 1/767/20400
= 1 × 20400/767 = 20400/767 days
= 26 458/767 days = or 26.597 days
Thus, Stephen, Justin, and Scott working together will finish the total work (1 work) in 26 458/767 days = or 26.597 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 Stephen = 75 days
And the number of days required to finish the same work by Justin = 80 days
And the number of days required to finish the work by Scott = 85 days
Thus, the number of days required to finish the work by Stephen, Justin, and Scott together = ?
Here a = 75 days
And, b = 80 days
And, c = 85 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Stephen, Justin, and Scott working together
= 75 × 80 × 85/75 × 80 + 75 × 85 + 80 × 85 days
= 510000/6000 + 6375 + 6800 days
= 510000/19175 days
= 510000/19175 days
= 510000 ÷ 25/19175 ÷ 25 = 20400/767 days
= 26 458/767 days or 26.597
Thus, Stephen, Justin, and Scott together will finish the work in 26 458/767 days or 26.597 days Answer
Similar Questions
(1) Andrew can finish a work in 41 days. Kenneth can finish the same work in 46 days while Kevin can finish the work in 51 days. How long will it take to finish it if they work together?
(2) Joshua can finish a work in 43 days. Kevin can finish the same work in 48 days while Brian can finish the work in 53 days. How long will it take to finish it if they work together?
(3) If Matthew can finish the work in 26 days and Edward can finish the same work in 30 days, then in how many days both can finish the work together?
(4) If Betty can finish the work in 27 days and Jason can finish the same work in 30 days, then in how many days both can finish the work together?
(5) Larry can finish a work in 77 days. Scott can finish the same work in 82 days while Brandon can finish the work in 87 days. How long will it take to finish it if they work together?
(6) If Amanda can finish the work in 48 days and Patrick can finish the same work in 53 days, then in how many days both can finish the work together?
(7) If Brandon can finish the work in 83 days and Joe can finish the same work in 88 days, then in how many days both can finish the work together?
(8) If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?
(9) If Ashley can finish the work in 33 days and Eric can finish the same work in 37 days, then in how many days both can finish the work together?
(10) Rachel can finish a work in 94 days. Janet can finish the same work in 99 days while Catherine can finish the work in 104 days. How long will it take to finish it if they work together?