Question 832254
let bhose be the time for Bob's hose and jhose be the time for Jim's hose, then
the contributions per hour is described by the following equation
1/bhose + 1/jhose = 1/18
also we know
bhose = jhose - .20jhose
note that 1/bhose represents how much work bhose does per hour and 1/jhose represents how much work jhose does per hour
knowing this let's substitute for bhose in our first equation
1/(jhose - .20jhose) + 1/jhose = 1/18
1/(.80jhose) + 1/jhose = 1/18
multiply both sides of = by jhose
1/.80 + 1 = jhose/18
2.25 = jhose /18
jhose = 2.25 * 18 = 40.5 hours
bhose = 40.5 - (0.20*(40.5)) = 32.4 hours
check the answer
1/32.4 + 1/40.5 = 1/18
0.03086419753086419753 + 0.02469135802469135802 = 0.05555555555555555556
0.05555555555555555556 = 0.05555555555555555556
answer checks