In a river that flows at 3 mph, a boat takes 1 hour longer to sail 36 miles upstream than to return. Find the speed of the boat in still water

Answer 1

36 = (R+3)*t

36 = R*(t+1)

(R+3)*t = R*(t+1)

Rt + 3t = Rt + R

3t = R

Substituting into the first equation:

36 = 3t(t+1)

36 = 3t^2 + 3t

12 = t^2 + t

0 = t^2 + t -12

0 = ( t + 4 )( t - 3 )

t+4 = 0 results in negative time

t-3=0 ---> t=3

Plugging into the first equation again....

36 = (r+3)*t

36 = (r+3)*3

12 = r+3

r=9

The speed of the boat is 9 mph.

going downstream, it goes 36 miles at 9+3=12 mph, so 3 hours.

going upstream, it goes 36 miles at 12-3 = 9 mph, so 4 hours.

That is in fact 1 hour longer.

The speed of the boat is 9 mph