Question 184033
Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r
Let t=amount of time used to travel upstream
And (5-t)= amount of time used to travel downstream

Distance travelled upstream=8*t
Distance travelled downstream=12(5-t)
And we know that the above two distances have to be equal, so:
8t=12(5-t) get rid of parens
8t=60-12t  add 12t to each side
8t+12t=60-12t+12t  collect like terms
20t=60
t=3 hr-----------------time travelled upstream
So, 7am + 3 hr=10am--------------time to turn back
5-t=5-3=2 hr ------------time travelled downstream
distance upstream =8*t=8*3=24 mi from resort

ANOTHER WAY:
let t=time used to travel upstream
Then 5-t=time used to travel downstream
Let d=distance travelled upstream; also distance travelled downstream as well as distance from resort when turning back
7am + t=time to turn back
t=d/8-----------------------------eq1
5-t=d/12---------------------------eq2
substitute t=d/8 from eq1 into eq2
5-d/8=d/12  multiply each term by 24
120-3d=2d  add 3d to each side
5d=120
d=24 mi----------------------distance from resort when turning back
substitute d=24 into eq1
t=24/8=3 hrs----------------time used to travel upstream
7am+3=10am-------------time to turn back



Hope this helps---ptaylor