# Question #dd61e

Nov 28, 2014

Let ${D}_{I}$ be the distance traveled by Ian
Let $x$ be Ian's speed.
Let $y$ be the duration that Ian traveled

${D}_{I} = x y$

Let ${D}_{H}$ be the distance traveled by Han

${D}_{H} = \left(x + 5\right) \left(y + 1\right)$
$\implies {D}_{H} = x y + x + 5 y + 5$

${D}_{H} = x y + 70$

$x y + x + 5 y + 5 = x y + 70$
$\implies x + 5 y + = 65$

Let ${D}_{J}$ be the distance traveled by Jan
Let $Z$ be the extra distance traveled by Jan compared to Ian

${D}_{J} = \left(x + 10\right) \left(y + 2\right)$

${D}_{J} = x y + Z$

$\implies x y + 2 x + 10 y + 20 = x y + Z$
$\implies 2 x + 10 y + 20 = Z$

$\implies 2 \left(x + 5 y\right) + 20 = Z$

$\implies 2 \left(65\right) + 20 = Z$

$\implies Z = 150$