Answer:
The easiest way to solve this system would be to use substitution since x is already isolated in the first equation. Whenever one equation is already solved for a variable, substitution will be the quickest and easiest method
Answer:
Jim's hose: 27 hours.
Bob's hose: 21.6 hours.
Step-by-step explanation:
Let t represent hours taken by Jim's hose.
Part of pool filled by Jim's hose in 1 hour would be
.
We have been given that Bob's hose, used alone, takes 20% less time than Jim's hose alone. This means that Bob's hose take will take 80% time of Jim's hose that is
.
Part of pool filled by Bob's hose in 1 hour would be
.
We are also told that it takes 12 hours using both hoses. Part of pool filled by both hoses in 1 hour would be
.
Now, we will add rates of both hoses and equate with
as:




Cross multiply:




Therefore, it will take 27 hours for Jim's hose to fill the pool alone.
Time take by Jim's hose alone:
.
Therefore, it will take 21.6 hours for Bob's hose to fill the pool alone.
Cos60 degrees=1/2, so AK/AB=1/2. Since AK=KD, AK=1/2AD=1/2AB. Therefore, AB=AD. This is a rhombus, with four equal sides. Triangle ABK is congruent to triangle DBK (SAS), since AK=KD, angle AKB=angle BKD=90, and BK=BK. Therefore, BD=AB. The sum of four side lengths is 24. Each side length is equal to 24/4=6. BD=6.