Question 255308
Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar.
 Together they can paint a given fence in 4 hr. 
How long would it take Pedro paint the same fence if he had work alone?
:
let t = time required by Pedro alone
then
1.5t = time required by Juan
and
1.2 = time required by Pilar
:
Let the completed job = 1
:
{{{4/t}}} + {{{4/(1.5t)}}} + {{{4/(1.2t)}}} = 1
Multiply equation by 6t, results
6(4) + 4(4) + 5(4) = 6t
24 + 16 + 20 = 6t
60 = 6t
t = {{{60/6}}}
t = 10 hrs for Pedro
1.5(10) = 15 hrs for Juan
1.2(10) = 12 hrs for Pilar
;
:
Check solution on a calc:
{{{4/10}}} + {{{4/15}}} + {{{4/12}}} = 1