Answer
$840$ miles.
Work Step by Step
Distance traveled in any of the two legs = (average speed)(time of travel).
Going distance = $50x,$
Return distance = $55(32-x)$.
Adding the times given in the table, we see that total time is 32 (x+32-x=32).
We solve an equation obtained from
(Going distance) = (Return distance)
$50x=55(32-x)$
$50x=1760-55x$
$105x=1760$
$x=\displaystyle \frac{1769}{105}\approx 16.762$
Going distance = $50x\approx 50(16.762)=838.1\approx 840$ miles.
