labor cost

Question

Mark and Rachel work for a landscaping company. Mark can finish a planting job in 3 hours and Rachel can finish the job in 4 hours. if they work together on the job and the cost of labor is 40 dollars per hour what should the labor estimate be?

Answer 1

Let's imagine that the planting area is a grid 12 units in size (since 3 * 4 = 12).

This means that Mark can do four units in an hour so that he finishes in three hours.

This means that Rachel can do three units in an hour so that she can finish in four hours.

This means that seven units are done in an hour when they work together (3 + 4 = 7).

 

7 units * x hours = 12 units

divide both sides by 7 units:

x hours = 12/7

 

Now the cost is $40/hour, and they work for 12/7 hours, so that means:

final cost = ($40 / hour) * (12 hours / 7)

final cost = $40 * 12 / 7

final cost = $480 / 7

final cost = $68.5714, or $68.57 to the nearest cent.

Answer 2

Mark does 1/3 of the job in 1 hour

Rachel does 1/4 of the job in 1 hour

let x=# of hours it takes them working together to finish the job

(1/3)x+(1/4)x=1 (job finished)

multiply both sides by 12

12(1/3)x+12(1/4)x=12(1)

4x+3x=12

7x=12

x=12/7 or 1 5/7 hours which is approximately 1.7 hours

the labor estimate is $40*1.7 hrs=$68

exactly the cost is $40*(12/7)=$480/7=$68.57 to the nearest penny