Answer:
It takes the second worker 11 hours to do the job alone
Step-by-step explanation:
The problem tells you how to work it.
x = 11 tells you the second worker takes 11 hours to do the job alone.
_____
You can also work directly with the fractions. Subtract 1/11 and you have ...
1/x = 1/11
It should not be a real stretch to see that x=11. If you need, you can multiply both sides by 11x to get 11=x.
We need to find the base x in the following equation:
First, lets convert 365 from base 7 to base 10. This is given by
where the upperindex denotes the position of eah number. This gives
that is, 365 based 7 is equal to 194 bases 10.
Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:
where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives
Now, we have all number in base 10. Then, our first equation can be written in base 10 as
For simplicity, we can omit the 10 and get
so, we can solve this equation for x. By combining similar terms. we have
and by moving 197 to the right hand side, we obtain
Finally, we get
Therefore, the solution is x=5
