Question

it takes a boat 3 hours to down a river from point A to point b and 5 hoursto travel up the river from B to A how long would it take the same boat to go to a to b in still water

Answer 1

3 3/4 hr

Explanation:

I had an 'aha moment' while I was out on a starlit run...(Check out the night sky just after sunset.(Northern hemisphere)...Venus and Jupiter are very near each other and BRIGHT....add the moon and Mars for almost a straight line !)

the time it takes up stream = 5 hours = distance / (r-s)

so d = 5 (r-s)

downstream = 3 hours = distance/ (r+s)

so d = 3(r+s)

Equate these two definitions of d

5r- 5s = 3r+ 3s

2r = 8s

r = 4 s so set a distance say 15 miles

then r = 4 and s = 1 to get 5 hrs and 3 hrs

if d = 15 and r = 4 the time for still water travel = 15/4 = 3 3/4 hrs

As another example say r = 6 then s = 6/4 then d = 22.5

22.5 / 6 = 3 3/4 hrs <===== same answer

So distance is NOT required to answer this question!