Question

A boat takes 4 hours to go 12 miles upstream. It can go 32 miles downstream in the same time. Find the rate of the current and the rate of the boat in still water.​ (Hint: Because the current pushes the boat when it is going​ downstream, the rate of the boat downstream is the sum of the rate of the boat and the rate of the current. The current slows down the boat when it is going​ upstream, so the rate of the boat upstream is the difference of the rate of the boat and the rate of the​ current.)

Answer 1

The speed upstream is the difference between the boat speed and the current speed. It is (12 mi)/(4 h) = 3 mph.

The speed downstream is the sum of the boat speed and the current speed. It is (32 mph)/(4 h) = 8 mph.

The speed of the boat is the average of these: (3 + 8)/2 = 5.5 mph.

The speed of the current is that less the difference: 5.5 - 3 = 2.5 mph.

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Check

Boat + Current = 5.5 + 2.5 = 8 mph

Boat - Current = 5.5 - 2.5 = 3 mph