Working a job

Question

John completes a job in 8 days. Same job can be done by Peter in 6 days. They work together for same job for two days the peter stops working, in how many days John completes the remaining job?

Answer 1

Let W be the number for Worker-Days to do the job.

Then for John R_{j *} 8 = W so R_j = W/8

For Peter R_p * 6 = W    So R_{p = W/6}

Working together for two days (R_j + R_{p) *2 = ( W/8 +W/6) *2 = ( W/4 +W/3) = 7W/12}

The remaining work will be W - 7W/12 = 5W/12

To find remaining days for John R_{j *d= 5W/12 = W/8 * d = 5W/12}

d= 8/W* 5W/12 = 40/12= 10/3 days

Answer 2

So, in two days, John is going to get 2/8 = 1/4 of the job done and Peter will get 2/6 = 1/3 of the job done.

 

1 - (1/4 + 1/3) = 1 - (3/12 + 4/12) = 1 - 7/12 = 5/12 of the job left.

 

(5/12)8 = 40/12 = 3 1/3 days