When will they finish and how much will it cost?

Question

Suppose you hire three 3-toed sloths to build a tree fort. Typically 3-toed sloths work alone and advertise as such. The signs indicate how long it takes them to build a fort individually and how much they charge per hour (24 hours, $5/hr. 16 hours, $10/hr. 12 hours, $15/hr.) If these sloths start at noon and work together, when will they finish and how much will it cost to build a fort?

Answer 1

In one hour the slow sloth does 1/24 of the job.

In one hour the middle sloth does 1/16 of the job.

In one hour the fast sloth does 1/12 of the job.

 

In x hours the slow sloth does x/24 of the job

In x hours the middle sloth does x/16 of the job

In x hours the fast sloth does x/12 of the job

 

Together they do the one job.

 

x/24 + x/16 + x/12 = 1             Multiple by LCM

2x + 3x + 4x = 48

9x = 48 

x = 5.3333333

 

They take 5 and 1/3 hour to complete the job.

 

At what time do they finish?

How much pay does each get?