Question 397853
Let {{{1/b}}} = rate that Bob's hose alone fills pool (1 pool/ b hrs)
Let {{{1/j}}} = rate that Jim's hose alone fills pool (1 pool/ j hrs)
Let {{{1/x}}} = rate that both hoses fill pool (1 pool/ x hrs)
Then
(1) {{{1/b + 1/j = 1/x}}}
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given:
{{{1/x = 1/24}}} (1 pool)/(24 hrs)
{{{1/b = 1/(j - .4j)}}}
(2) {{{1/b= 1/(.6j)}}}
and, from (1)  
(1) {{{1/b + 1/j = 1/24}}}
These are 2 equations and 2 unknowns, so it's solvable
By substitution:
{{{1/(.6j) + 1/j = 1/24}}}
Multiply both sides by {{{.6j}}}
{{{1 + .6 = (.6j)/24}}}
{{{.6j = 24 + 14.4}}}
{{{j = 38.4/.6}}}
{{{j = 64}}}
and, from (2),
{{{1/b = 1/(.6*64)}}}
{{{1/b = 1/38.4}}}
{{{b = 38.4}}}
Bob's hose alone takes 38.4 hrs
Jim's hose alone takes 64 hrs
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check answer:
(1) {{{1/b + 1/j = 1/24}}}
{{{1/38.4 + 1/64 = 1/24}}}
{{{1/384 + 1/640 = 1/240}}}
I'll just convert to decimals:
{{{.002604167 + .0015625 = .00416667}}}
{{{.004166667 = .00416667}}}
close enough