Answer
Jim's hose: 40.5 hours
Bob's hose: 32.4 hours
Work Step by Step
Using both hoses: 18h
Jim's hose: x
Bob's hose 0.8x=$\frac{4}{5}$x (20% less time than Jim's hose)
Fractions of pool they will fill in one hour:
Both hoses together: $\frac{1}{18}$
Jim's: $\frac{1}{x}$
Bob's: $\frac{1}{\frac{4}{5}x}$=$\frac{5}{4x}$
Equation:
$\frac{1}{x}$+$\frac{5}{4x}$=$\frac{1}{18}$
mulitpy by 36x
36+45=2x
81=2x
x=40.5
0.8x=32.4
