Answer
1,830,000 miles is the maximum distance that Ganymede can be from Jupiter and still cause a total eclipse.
Work Step by Step
Let $D_J$ be the sun's distance from Jupiter and let $D_S$ be the sun's diameter. Let $d_J$ be Ganymede's distance from Jupiter and let $d_G$ be Ganymede's diameter.
Using similar triangles, we can find the maximum distance that Ganymede can be from Jupiter and still cause a total eclipse:
$\frac{D_S}{D_J} = \frac{d_G}{d_J}$
$d_J = \frac{d_G~D_J}{D_S}$
$d_J = \frac{(3270~mi)(484,000,000~mi)}{(865,000~mi)}$
$d_J = 1,830,000~mi$
1,830,000 miles is the maximum distance that Ganymede can be from Jupiter and still cause a total eclipse.
