Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar and together they can paint a given fence in 4 hours. How long will it take Pedro to paint the same fence if he had to work alone?

Solution:

Let Rate of pedro = 1/t_{pedro} = x

Rate of juan = .50x

Rate of pilar = .80x

(x+.50x+.80x)4=1

2.3x=1/4

x=5/46

5/46 = 1/t_{pedro}

t_{pedro}=46/5 =9.2hours

Is this solution correct because the book says the answer is 10hours.

Consider these:

Rate of Juan = (2/3)*Rate of Pedro

Rate of Pilar = (5/6)*Rate of Pedro

Thank you sir. Just now i can see my analyzation is very wrong.