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Man-Hours Word Problems / Time Work and Men

A man-hour is the work done by one worker in an hour. For time and work-related problems, we assume that all workers or machines are equally efficient which means, every person/ machine finishes equal amount of work in equal span of time unless specified otherwise.


Work done or task can be expressed in terms of man-hours.

  • Work done/task = number of hrs h taken by m men to complete the task = m x h

a) 1 man working for 3 hours = 1man x 3hrs = 3man-hours

b) 2 men working for 3 hrs = 2men x 3hrs = 6man-hours

  • If we double the number of men , twice the work can be done in same time.

a) 2 men working for 1 hour + 1 man working for 3 hrs= (2×1)+(1×3) man-hours

  • Work done is directly proportional to number of men m and number of hours h.

a) When both days and hrs are given then hrs = days x hrs per day


Example

How much time will two men take to complete a task ,if six men complete the same

task  in 12 hrs ?

Solution:

Using Logic:

If 6 men take 12 hrs then 1/3rd  of the men ie two men , will take 3 times the original

time. Therefore, time required = 3 x 12 =36 hrs

Using Formula:

Task requires  6 men x 12 hrs = 72 man-hrs

Same task can be done by 2 men in h hrs , 2 men x h hrs = 72 man-hrs

h hrs = 72man-hrs/2 men = 36 hrs

Two men will take 36 hrs to complete the task.

Example:

Twelve machines work twelve hours a day to complete a task .

  1. How many machines will be required to finish double the task in the same time?
  2. How many machines will be required to finish the task in same time if four of the machines broke down after 3rd hour?

Solution:

Using Logic :

Let number of machines be y.

a) 12 machines complete the task in 12 hrs. Double the machines are required to finish double the task in the same time. Therefore, number of machines required to complete double the task = 24 .

b) 4 machines worked for 3 hrs = 12 machine hrs – work of one machine in 12 hrs

To finish the task 4 machines should have worked for 12 hrs = 12 X 4 = 48 machine hrs. Therefore, 12 machines + 3 extra machines = 15 machines.

Using Formula:

Let number of machines be Y.

a) Task = 12 machines x 12 hrs = 144 machine hrs

Double task = 2 x 144 hrs = 288  machine hrs

288 machine hrs = Y machines X 12hrs

Number of machines Y = 288 machine hrs/ 12 hrs = 24 machines

 

b) Task = 12 machines x 12 hrs = 144 machine-hrs

     144 = (4 machines x 3 hrs ) + (Y-4) machines  x 12 hrs

           = 12 machine hrs + 12 Y machine hrs  – 12 x 4 machine hrs

     144 = 12 y machine hrs – 36 machine hrs

     180 machine hrs = 12 Y machine hrs

     Y= 180 machine hrs/12 hrs  = 15 machines  

 

Example:

A road can be constructed by twelve employees working eight hours a day for thirty days. To speed completion of the project , a contractor deploys 30 employees to complete the project in sixteen days. How many hours a day must the employees work , in order to finish the construction work?

Solution:

Using logic:

Number of men in 1st case= 12

Number of men in 2nd case=30

Number of men in 2nd case is 2.5 times more than that in 1st case.

Therefore, number of hrs in 1st case will be = 2.5 x number of hrs in 2nd case

i.e. 30 days x 8 hrs = 2.5 (16days x h)

h = 30×8 / 2.5×16 hrs = 6hrs

Using Formula:

Construction is done by 12 men in 30 days working 8 hrs a day

Construction of road  is Work W = man x hrs = man x (days x hrs)

                                            = 12 men x 30 days x 8 hrs

                                            = 2880man hrs

Construction of same road by 30 men takes h hrs per day for 16 days

 W = 2880 man-hrs = 30 men x 16 days x h hrs

 h = 2800 man-hrs / (30 men x 16) = 6 hrs