Time and work
Algebra
Level
3
Person A can lay a railway track between two given stations in 16 days and Person B can do the same job in 12 days.
With the help of Person C, they did the job in 4 days only. Then, Person C alone can do the job in how many days?
The answer is 9.6.
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1 solution
Person A can lay the track in 16 days, so in 4 days they lay 1/4 of the track. Person B can lay the track in 12 days, so in 4 days they lay 1/3 of the track. This means together they lay 1/3 + 1/4 = 7/12 of the track, so Person C lays 5/12 of the track in 4 days.
This means that in Person C takes 1/12 of the track in 4/5 (0.8) days, so they lay 12/12 (all) of the track in 0.8*12 = 9.6 days.