Problema Solution
after 5 hours of house painting, jess asked the assistance of john. together they finished the job in 4 more hours. had jon join in an hour afetr jess started working, the job would have been finished in seven hours. How long would it have taken jess to paint the house alone?
Answer provided by our tutors
let
x = the hours that jess needs to finish the job alone thus his rate is 1/x houses per hour
y = the hours that jon needs to finish the job alone thus his rate is 1/y houses per hour
after 5 hours of paint work, jess ask jon to help him and they finish the job in 4 hours
5/x + 4(1/x + 1/y) = 1
if jon joined jess after an hour of work they would have finished the job in 7 hours
1/x + 7(1/x + 1/y) = 1
lets substitute a = 1/x and b = 1/y we have the following system of equations
5a + 4(a + b) = 1
a+ 7(a + b) = 1
by solving we find
a = 3/31
b = 1/31
click here to see the step by step solution of the system of equations
x = 1/a
x = 31/3
x = 10 h 20 min
y = 1/b
y = 31 h
Jess needs 10 h 20 min ti finish the work alone.