Work problems

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/tpedro = x
Rate of juan = .50x
Rate of pilar = .80x
(x+.50x+.80x)4=1
2.3x=1/4
x=5/46
5/46 = 1/tpedro
tpedro=46/5 =9.2hours

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

Jhun Vert's picture

Consider these:

  • 1.50*Rate of Juan = Rate of Pedro
    Rate of Juan = (2/3)*Rate of Pedro
  • 1.20*Rate of Pilar = Rate of Pedro
    Rate of Pilar = (5/6)*Rate of Pedro

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

how it became 1.50 and 1.20?

Jhun Vert's picture

50% faster is 100% + 50% or 1.5.

where did the 2/3 and 5/6 came from

Jhun Vert's picture

calculator... 1 ÷ 1.5 = 2/3