Question 112212
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r

Let d=distance of the farm from Duane's home

Time it took Duane by car (going)=d/54
Time it took Duane by Motorcycle (returning)=d/36

Now we are told that the sum of the above two times equals 4 hours.  So:

(d/54)+(d/36)=4   multiply each term by 108 (LCM)

2d+3d=432
5d=432  divide both sides by 5

d=86.4 mi---------distance of farm from Duane's home

CK
(86.4/54)+(86.4/36)=4
1.6+2.4=4
4=4


Hope this helps--ptaylor