Whole trip takes 50 minutes or 50/60 hours = 5/6 hours

Temptation is to notice 8 and 6 average to 7 km/hour so

distance equals rate of speed times time would give 7 times 5/6= 35/6

as total distance. That's close, a good approximation, but

since the 8 km/hr driving time is less than the 6 km/hr time, the 7 km/hr

approximation is weighted slightly on the higher side.

Let x = the time to drive the 8 km/hour distance, so 8x=the distance

then let 5/6-x = the time to drive the 6 km/hour trip then 6(5/6-x) is the same distance

Set them equal: 8x=6(5/6-x) and solve for x The distance is the same from either direction

8x=5-6x

14x=5

x=5/14

8x=8(5/14)=40/14=20/7

that's half the distance, so double it to get the full total distance of 40/7

we originally estimated 35/6 as the total distance.

35/6 compares to 40/7 very closely

but 35/6 overestimates it slightly, as 35/6 is greater than 40/7

35/6=245/6 while 40/7 = 240/7, just 5/7 greater

The correct answer is 40/7 = about 5.71 or exactly 5 5/7 km