Answer
Jerome takes 10.5 hours, Tim takes 9.5 hours
Work Step by Step
Jerome takes $x$ hours, Tim takes $x-1$ hours
$1/x + 1/(x-1) = 1/5$
$x(1/x + 1/(x-1)) =x* 1/5$
$1+ x/(x-1) = x/5$
$(x-1)(1+ x/(x-1)) = x/5*(x-1)$
$(x-1) + x = x*(x-1)/5$
$2x-1=x*(x-1)/5$
$5*(2x-1)=5*x*(x-1)/5$
$10x-5 = x*(x-1)$
$10x-5=x^2-x$
$x^2-x=10x-5$
$x^2-x-10x+5=10x-5-10x+5$
$x^2-11x+5=0$
$a=1$, $b=-11$, $c=5$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-(-11)±\sqrt {(-11)^2-4*1*5})/2*1$
$x=(11±\sqrt {121-20})/2$
$x=(11±\sqrt {101})/2$
x=(11±10.049)/2$
$x=(11+10.049)/2
$x=21.049/2$
$x=10.52$
$x=(11-10.049)/2$
$x=.951/2$
$x=.475$
We disregard this answer since this would result in Tim’s time being negative, and we can’t have negative time.
$10.5-1=9.5$
