# Assumption: a can work in 10 days.B can work in 15.so the days in which both will finish are 6.

#### harshk

##### New member
Ques- a can work in 10 days.B can work in 15.so the days in which both will finish are 6. Here we have assumed the complete work as 100% or 1 or the LCM,etc and we still get the same answer always i.e 6 no of days.If i assume total total work as 83.3 then also it'll be 6. So my question is if we assume different things in maths why not answers of all those threads different.

#### Dr.Peterson

##### Elite Member
Ques- a can work in 10 days.B can work in 15.so the days in which both will finish are 6. Here we have assumed the complete work as 100% or 1 or the LCM,etc and we still get the same answer always i.e 6 no of days.If i assume total total work as 83.3 then also it'll be 6. So my question is if we assume different things in maths why not answers of all those threads different.
The problem, stated more clearly, is,

If A can complete a certain task in 10 days and B can complete it in 15 days, then how long will it take if both work together, each at the same rate they work alone, without helping or interfering with one another?​

The amount done together will be 1/10 X + 1/15 X = 1/6 X, where X is some measure of the size of the task; therefore it takes 6 days to complete that task (6 * 1/6 X = X).

We often measure the task in terms of "number of tasks", so that completing the task means X = 1 task. But we can measure it in any unit you wish, including, say, X = 83.3 kilometers, or X = 83.3 kilograms, or whatever. It doesn't matter what unit you use, or what number you use for the measure of the task, because X cancels out.

Another way to do this is to say that in T days, they will accomplish T/10 + T/15 = T/6 of the task, so they will do 1 task when T = 6 days. Here I didn't use any measure of the task, just a fraction.