The boat, moving in a straight line at a constant speed relative to the water, travels a path s between

The boat, moving in a straight line at a constant speed relative to the water, travels a path s between two points on the river downstream at a time t1 = 30 min, back in t2 = 45 minutes, how long t would the boat take to cover this distance in still water

When moving against the stream of the river, the speeds of the boat and the river are subtracted, and added downstream. We denote by v and x the speed of the river and the boat, respectively, then we get the system of equations:

S / (x – v) = 3/4;

S / (x + v) = 1/2.

3 (x – v) = 4S;

x + v = 2S.

Let us express v from the second equation:

v = 2S – x.

We substitute in the first:

3 (x – 2S + x) = 4S;

6x = 10S;

x = 10 / 6S.

Then the time to overcome the distance S in still water is:

S: 10 / 6S = 6/10 hours.

Answer: the required time is 6/10 hours or 36 minutes.