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 & 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
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