Problema Solution
julius can paint a house three times faster than ruben. working together they can paint a house in 4 days. how long would it take the faster painter if he works alone?
Answer provided by our tutors
let
x = the time Julius needs to paint the house alone
y = the time Ruben needs to paint the house alone
together they finish the house in 4 days
Julius can paint a house three times faster than Ruben
y = 3x
in 1 day Julius will finish 1/x house, x>0
in 1 day Ruben will finish 1/y house, y>0
in 1 day Julius and Ruben finish 1/4 of the house
1/x + 1/y = 1/4
by solving the system of equations
y = 3x
1/x + 1/y = 1/4
we find
x = 16/3 days = 5 days 8 hours
y = 16 days
the faster painter will finish the job in 5 days and 8 hours.