# Dad and son both work a certain job that they finish in 12days. After 8days the son gets sick. To finish the job dad has to work 5 more days. How many days would they have to work to finish the job, if they work separately?

##### 2 Answers

The wording presented by the question writer is such that it is not solvable(unless I have missed something). Rewording makes it solvable.

#### Explanation:

Definitely states that the job is "finished" in 12 days. Then it goes on to say by (8+5) that it takes longer than 12 days, which is in direct conflict with the previous wording.

ATTEMPT AT A SOLUTION

Suppose we change:

"Dad and son both work a certain job that they finish in 12 days".

Into:

"Dad and son both work a certain job that they anticipate to finish in 12 days".

This enables the 12 days to change count instead of being fixed.

Each of the father and son could contribute different amounts of output to achieve the final total output.

Thus

Let the amount of work done in 1 day by the son be

Let the amount of work done in 1 day by the farther be

Let the total amount work needed to achieve the end product be

Condition1

The original anticipated contribution without son being sick

Condition2

The actual contribution with the son being sick

These can now be solved in the normal way as simultaneous equations

The position in the question of the wording "farther had to work 5 more days" implies that the 5 days commence from, and includes, the day after the son falls sick.

Under these assumptions a solution is now obtainable.

If my assumption about the question wording is wrong then you need to seek guidance from another source.

Father needs to work 15 days and son 60days.