We will assume the average rate of the travel is constant.

Let

v = the average rate

d1 = 260 mi the distance to the uncle's house

d2 = 364 mi the distance to the Grand Canyon

t1 = 5 hr the time of the travel to the uncle's house

t2 = the time of the travel to the Grand Canyon

Since average rate = distance/time we have:

v = d1/t1 but also v = d2/t2

Now we can write:

d1/t1 = d2/t2

260/5 = 364/t2

364/t2 = 260/5

........

click here to see the equation solved for t2

........

t2 = 7 hr

It would take 7 hours to drive to the Grand Canyon.