Question

A finishes a job in 10 days. B finishes in 15 days. If A and B work at it together, how many days will they take to complete the job? ​

Answer 1

Answer:

The obvious first answer:

(10 + 15)/2 == 12.5

Seems legit. But it is o obviously incorrect. Time of first worker alone is less than this.

There would be one edge case where this incorrect formula would give proper result: when speed of work #1 is exactly the same as speed of work #2.

Correct explanation would be this:

Whenever you have Work (Path), Speed and Time you should know all these ideas are tight together in equation:

S = V*t (*)

S - Path (or work in our case)

V - Speed of travelling (or work)

t - time required to complete whole piece of work (or path the whole path).

First worker: his speed is v1, time required: t1

Second worker: his speed is v2, time required t2

Taking into account (*) we get:

v1 = S/t1

v2 = S/t2

Both of them do the job with speed:

v3 = v1 + v2 = S/t1 + S/t2;

Now, again, taking into account (*):

t3 = S/v3 = S/(v1+v2) = S/(S/t1 + S/t2) = S/(S*(t1 + t2/t1*t2)) = t1*t2/(t1 + t2)

Now.

t1 is 10 and t2 is 15.

So:

t3 = 10*15/(10+15) = 6.

PS:

All the above is correct only if there is no dependencies between workers and their job, none of them could possibly block each other, none of them does not rely on certain pieces of other`s job parts, etc.

Answer 2

Step-by-step explanation:

A complete 1/10th of the work in one day.

B complete 1/15th of the work in one day.

Therefore, A and B complete 1/10 +1/15 = 10/60th work in one day.

Thus, it will take 10/60=6 days to complete the work by both A and B.

Hope this will be helpful.