Answer:
20 hours
Step-by-step explanation:
rate and time are inverses of each other.
If it takes one 36 hours, so his rate is:
1/36
It takes another 45 hours, so his rate is:
1/45
Since they will work together, their combined rate will be:
1/36 + 1/45
Now, we want the TIME IT WILL TAKE THEM, so we inverse their combined rate, that is we take the combined rate and raise it to -1st power. The calculation is shown below:
[tex](\frac{1}{36}+\frac{1}{45})^{-1}\\=(\frac{45+36}{45*36})^{-1}\\=(\frac{81}{1620})^{-1}\\=\frac{1620}{81}\\=20[/tex]
Thus, if both work together, it will take them 20 hours
