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.